Tuesday, February 28, 2006 

Who's been playing Grow? How close have you guys come to maxing everything?? This is the closest I've come. The game is starting to annoy me. :P





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Scribe

Hi it is me. i hope none of you knows me.I am today's scribe and here are details of what we did in class today.
1) Factorial Notation:
Definition:- n!=n(n-1)(n-2)(n-3)......3-2.
0!=1
Examples: 4!=4.3.2.1 6!=6.5.4.3.2.1
= 24 =720

on the TI83: 6! then punch 6 on the main screen then press(Math) then (<) then(4) then (Enter) Note: Factorial notation is not defined for negative numbers. i.e (-3)! is undefined. Permutation: A permutation is an ordered arrangement of objects. Formula: nPr=n1/(n-r)! [often called the "pick" formula] n is the number of objects to choose from r is the number of objects to be arranged nPr is read as: 1)"n permute r" OR 2) "n pick r" nPr means: Given a set of n objects. How many different arrangements can you make using only r of them at a time. Example 1) 6P2=6!/(6-2)!
=6!/4!
=6.5.4.3.2.1/4.3.2.1
=6.5
=30

Example 2) There are 8 horses in a race. In how many different ways can they finish 1st, 2nd and 3rd?
Solution 1): By the fundamental principle of counting.
8.7.6=336
Solution 2): As a permutation
8P3 = 8!/(8-3)!
=8!/5!
= 8.7.6.5.4.3.2.1/5.4.3.2.1
= 336
Permutations of Non-Distingiushable objects.
The number of ways to permute n objects which contain K1,K2,K3......... Non-Distinguish object is given by:
n!/K1!K2!K3!
Example: How many different "words" can be made from the letters of the word:
a)Book b) Mississippi
#Letters:4 #Letters:11
#o,s : 2 #I,s:4
4!/2! #S,s:4
4.3.2.1/2.1 #P,s:2
=12 11!/4!4!2!
=34650.
All the above are notes that we copied down in to our dictionaries today.(Good luck With That)

And Further more:I expect every one to know the meaning of permutation(Means That order Matthers)
That is all important stuff we did in class today.
We also found out the probability of winning 649.
If you had to pick from 49 factorial Y=yes N-No (NNN............YYYYYY)
The formula to find the probability = 49!/6!43!=13983816
which shows that the probability of winning a 649 is 1 out of 13983816 (This is a code word Which means don,t waste money on lotto 649)
Homework: Page 23 Question 1-6.
Thats all for today folks.

Note: Sorry i forgot to choose scribe for tomorrow.
Jessica is tomorrows scribe.




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Monday, February 27, 2006 

The Flip Site and Probability Links







Here it is: The Flip Site. Click on the guy in the striped shirt to see him flip the coin. He's been filping it once every five seconds since midnight, January 1, 2006. (He starts over again every new year.) It may also be interesting to explore the streaks link and watch the changing probabilities.






And, in the Theatre of Mathematics ...



And in the Tutorial Room ...




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Scribe
Wednesday 22, 2006



We did nothing much today. Mr.K. gave a little insight on Probability and talk about how it applys on our daily lives. He used this examples like winning a 649, hit by lightning twice, etc. Later that day (second peroid class) he kindly gave us time to work on the project because some poeple are having problem about the SPREAD SHEET. He helped that people that are having trouble.




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Scribe

Scribe
Wednesday 22, 2006


For those who were'nt able to come to class on Wednesday here it is. Mr. K start off our new topic,PROBABILITY. We did this little activity where we have to toss 3 coins (3 pennies) 30 times and we have to write how many times we got, exactly, 2 heads. One person got 16, highest, one person got 5, lowest, and 4 poeple got 10 which is the most. We haven't write anything that much, but here are some.

This is the theory that we came up with:
h = heads
t = tails

h t

h t h t

h t h t h t h t

hhh hht hth htt thh tht tth ttt


3 out 8 chances that, exactly, 2 heads and 1 tail will show up. This is how you set it up:

Formula for PROBABILITY:

3 = Is the chance of getting exactly 2 heads and 1 tail

8 = Is the total # of event that can happen

P(e) = The number (#) of favourable outcome/The total (#) of outcome

P(e) = 3/8

0.375 = 3/8

Probability can be written in:

Decimal = .375

Fraction = 3/8

Ratio = 3/8

I hope you get something from this!





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Probability

Hey guys its me rein, for today we had two math periods. In the morning class Mr. K put us into groups and worked on a probability excersice and we spent the whole morning class just to solve and understand the problem. To start the afternoon class Mr. K made us draw a tree diagram for flipping a coin ( 2 times and 3 times) and list the sample space (a sample space is the set of all possible things that can happen for a given set of circumstances.) and make a chart for rolling a 6 with dies ( one blue and one red). Our teacher also said that a tree diagram is better than a chart because a tree diagram breaks down or stratifies ideas in progressively greater detail. The objective of a tree diagram is to partition a big idea or problem into its smaller components, making the idea easier to understand or the problem easier to solve.
Note:1) When working with a tree diagram we MULTIPLY inorder to get the outcome.
For example: flip a coin two times the result must be two heads. To solve this problem this is what we have to do. We all know that when we flip a coin the probability is 50% (1/2)on getting heads and 50% (1/2) getting a tails. To find the outcome of this problem we have to multiply each of the possibility that we will get heads on the first flip and on the sencond flip. (REMEMBER: the posibilities dont change after the first flip)
(1/2) X (1/2)= 1/4 The answer is 1/4 or 25% chance of getting two heads in a row.
2) When collecting the sampe space we all add the possible outcome. For example, when flipping a coin two times the sampling space is 4 because their are 4 possilbe outcome ( Heads and Heads, Heads and Tails, Tails and Heads, Tails and Tails).
Near the end of the class he tought us some thing new and its called fractorial (dont know if i heared him correctly). The symbol for a fractorial is ! Which is equal to 12-11-10-9-8-7-6-5-4-3-2-1. To find this symbol on your calculator you go Math then go to the PRB section and press 4 or scroll down 4 times. He will talk about this more later on the course.
The homework for today is Page 17-19 numbers 1-9.
The next scribe is Khan. (If you did not understand any of my examples please feel free to ask Mr.K and he will be happy to help you :). )




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Testing

Testing




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Sunday, February 26, 2006 

Let It Grow Sunday!

This week's game is called Grow.



Draw each item to the center of the ball to Grow it. If you drag them in the right order you will reach the maximum growth level for each object -- that's the challenge and it's not easy. ;-) Lots of trial and error. The number of different ways to play this game is 479 001 600. Can you find the winning strategy?

The Applied Math class will learn how to figure this out this week. Pre-Cal will learn it in about two more months and the AP Calculus students should remember from the Pre-Cal class. Do you?

Have Fun!




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Friday, February 24, 2006 

blogging on blogging

In yesterday's math class we learned a few things about Pascal's Triangle, a.k.a. The Precious Mirror of the Four Elements, which is what Shi Cheng called it until the name was changed to Pascal's Triangle. That triangle really intrigued me, and I think that triangle is cool, for it had many interesting connections with many things. Some things didn't even have to relate to math.
That triangle is also like a calculator. You can find, powers of 2, powers of 11, triangular numbers, tetrahedral numbers, hexagonal numbers, pentatope numbers, Fibonacci numbers, and so forth. What suprised me was there was a familiar number in that triangle which had a connection to biology. That number being, 14641, which deals with skin pigmentation. There are, most likely, more things about that triangle we haven't learned about yet in class.
Well that triangle is something that I've learned about that I thought was cool. Hopefully we'll get to learn more about that triangle. And hopefully there will be tonnes more of interesting stuff that we'll be learning during this topic on Probability.




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Applied Math 40S: bloggong on blogging

Applied Math 40S: bloggong on bloggingso far i think this chapter "Matrix" was pretty easy for me, but once we got multiplication i got lost,but Mr:K adviced me to use my fingers and that was fun...the other thing that i like for Matrix is kind of topic that enjoy when i'm in class or when i'm doing my home work. first, it seems like difficult but it's not that hard trust me, all what you need it is just feel it and concentrate what you are doing that's all.




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Thursday, February 23, 2006 

bloggong on blogging

I"m kinda glad that matricies was our first unit in math this semester. I don't know about everybody else but I found that I understood it pretty easily. I never really had a problem with it. I think its kinda cool how matricies relate to so many things and could be used so many different ways. Well thats all i gotta say about the matricies unit. I just hope I understand the rest of the material in math this year as well as I understand matricies.




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Scribe February 23, 2006

Hi, for today's class we've study about the amazing Pascal's triangle or also called as The Precious Mirror of the Four Elements. What's amazing in this triangle is it can give a lot of information, for example, the answer to the number to the power of 2 it can be found by adding all the numbers every row. Also the number 11 to the power of 1,2 ,3 , 4 and so on it was exact number in every row of the triangle like 11 to the power of 0 is 1, 11 to power of 1 is 11, 11 to power of 2 is 121, 11 to power of 3 is 1331 and so on. We can also find triangular numbers, natural numbers, hexagonal numbers, pentatope numbers, fobonacci number, catalan numbers and tetrahedral numbers. here is how Pascal's triangle looks like
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
The next row can be found by adding the numbers in between from the last row of numbers and the next row must be begins and end with number 1. So the next row of the triangle above would be 1 7 21 35 35 21 7 1 and the process continue forever....
For those who missed the class here are the notes
PROBABILITY: The branch of mathematics that deals with chance
SAMPLE SPACE: The set of all possible things that can happen for a given set of circumstances
example: rolling a die-6
sample space would be (1, 2, 3,4,5 and 6) because this is all the possible outcomes
EVENT (E): An event is a subset of the sample space. It is one particular outcome for a given
set of circumstances
SIMPLE EVENTS: The result of an experimental carried out in 1 step
example: flip a coin. The result is Head
COMPOUND EVENT: The result of an experimental carried out in more than one step
example: Flip a coin and roll a die. The result is head and number 6
CALCULATING THE PROBABILITY OF AN EVENT......FORMULA:
P(E) = NUMBER OF FAVOURABLE OUTCOMES divides by
THE NUMBER OF POSSIBLE OUTCOMES (SAMPLE SPACE)
PROBABILITY CAN BE EXPRESSED AS:
  • A ratio
  • A Fraction
  • A decimal
  • A percent
CERTAIN EVENTS: An events whose probability is equal to 1.
IMPOSIBLE EVENTS: An event whose probability is equal to 0.
IMPORTANT: Probability is always a number between 1 and 0.
FUNDAMENTAL PRINCIPLE OF COUNTING:
If there are M to do a first thing and N ways to do a second thing, then there are M x N
ways to do both things.
Example:
How many outfits can be made from 3 pants and 4 shirts?
solution: 3 pants x 4 shirts = 12 different outfits
NEW CALCULATOR TECHNIQUE:
This is use to experiment something using a calculator.....
Experiment the probability of getting exactly 2 heads on fliping 3 coins 30 times
We knew that the theoretical probability is 3/8 so here is how to do the experiment on calculator.
Step
  1. Press math button on Ti83 calculator
  2. Select probability
  3. Select randBin (random binomial experiment)
  4. type in (1, 3/8, 30) 1 represent success, 3/8 represent theoreticall probability and 30 represent number of times it was done
  5. Press enter and a result will show in row
  6. press STO butoon to store the result
  7. press 2nd function STAT
  8. Select MATH then Sum
  9. this is to get all number 1 or the success

for next scribe Rein




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Wednesday, February 22, 2006 

Bloooogggg.

First of all cool...our blog is multiligual.....anyways...

What I've learn about matrices is pretty a lot, first it was confusing why learning all this stuff when i actually can't get money from it....hahahaha..but everything changed...matrices is actually a significant topic in math...it really applies math in it....In transition matrix first i was struggling to learn it...because i wasn't in class by the time they were learning it....I'm actually a lazy type of student satisfied with a 50 percent grade....but since i was in this class.. i think applied is easy to learn...trust mee i hated applied eversince grade 10....because of our introduction topic of matrices i was interested...and chose to go to class everyday...i just think matrices is a fun topic.it..twist your mind..but you need to twist it back to get it.... i think i'm writting a story now... butt anywayss.. that'ss ittttttttttttt. Hopefully I'm able to get all the questions this friday for the test.




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blog

I thought the matricies topic was fun and interesting at the beginning because it was really easy but then once we got more into depth with it, with the multiplying, it got more difficult for me and it started to confuse me. When you, Mr. K showed us how to multiply it with our hands it was confusing at first but I eventually got it after a couple of practice questions. The questions I liked the most was the network matricies and building the network diagrams. I thought it was sort of like solving a puzzle, when we had to build the matrix from the network diagram. The transition matricies and state matricies was what I had trouble the most with because I would get confused on which would be the state matrix or transition matrix and what numbers go here and what numbers go there but I think that im starting to uderstand them. I just need a little more practice.




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Tuesday, February 21, 2006 

something "cool"...

A comment on something that you've learned that you thought was "cool".


The cool thing I thought was the connectivity activites that we learned and did. Doing the direct routes kind of questions were pretty easy, but as we were given questions that had us figure out different routes like trying to get to a city by getting there in more than one way, kind of got tricky, but that was still cool since we got to think of other ways. It's cool cause what we're learning, its what airports, buses, and other ways of transportation go by, matrices. The 'one hop' 'two hop' 'three hop' and so on, kind of got me there. But i get it now, how if theres 2 stop overs that means theres 3 cities because your leaving from your city and you make the first stopover and thats one, then you get going and you make it to your destination which is your second and final stopover. I know Cait went over it again, but just reviewing!! This connectivity part of our unit is really helpful, we can apply this to our real lives, now or sometime in the future.Hmkai, laters!




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Blog

Matricies have been easy for me and I didn't have a lot of problems understanding them. But on page 91 in the textbook, there is this ONE problem that i'm having difficulty with. It is question 6 b) Determine the percent increase for each province from 1998 to 1999. I would greatly appreciate it if that question can be solved anytime during class.




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Tell Your Parents the Blog is Multilingual!

You'll notice that all posts on our blog now have a series of flags automatically added to the bottom. Click on a contry flag to have the blog translated into that country's language. You can choose from:

French, German, Italian, Portugese, Spanish, Japanese, Korean, Chinese and Filipino

If you speak any of these languages, let me know if they work well enough to be understood. And tell your parents all about it! ;-) Encourage them to leave comments on the blog as well.




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Blogging on Blogging

so far matrix looks like the easy chapter we have covered. titles covered includes: matrix addition, subraction and multiplication. let begin by defining matrix. which will be easy question if it will be on the test. matrix is a list of numbers arranged in columns and rows contained in square brackets. we don't want to make this an essay you can read your notes.

ex: [x x xx x x x x x x x x]
[x x x x x x x x x x x x]


let me get to the point. i understood the matrix chapter. but before that. i need to ask 2 questions if possible can be solved in class before the test.

qestions #9) b. determine the number of ways one person can contact another and use exactly 2 intermediaries.
and question #10. letters b and c
b. use the transition matrix to predict the probabilities for a customer's second visit to the library.
c. predict the probabilities for a customer's third visit.
both questions are on page 92 of the review questions.




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Monday, February 20, 2006 




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sorry i forgot to mention who is going to do tomorrows scribe.

Jessie_boy for tomorrows scribe. feb,21,06.




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blogging

So far, I've got a pretty good understanding of everything we've done on matrices.
Something that I found hard but now understand, was the question about 'stopovers' on the pre-test that we had on friday. I was very relieved when Cait said that she didn't know what the explanation was because in class today Mr. K went over it * THANKS Cait =) * .

The question asked: A network matrix, N, shows direct routes between cities. Which matrix calculation determines the number of routes with exactly k stopovers between two cities in the network? The answer was c) Nk + 1. See the thing is, N represents the direct routes. but we want to know what matrix is correct when using 'k' stopovers. Basically, the number of routes there are, is one less than the number of cities.

For example;
If you were trying to get from city A to city D, but there were no direct flights from A to D and you had to go through city B and city C...then that would mean that city B and city C are the two stopovers and city D is the destination which is the plus one.

So:
[city b and city c] = 2 stopovers = k    
and [city d] = destination = +1


So..if I understood right, from the 4 cities (A, B, C, and D), there would technically be 3 'stopovers'...?

So if there were 5 cities, there would be 4 stopovers.
If there were 20 cities, there would be 19 stopovers.
And vice versa, if there were 15 stopovers, there were 16 cities.

When Mr. K explained the whole thing, then kept giving examples like those, it suddenly clicked! Well, I'm not entirely sure if I actually explained it correctly, but I think I get it now.

Oh, there was also one more thing that i'm not very clear on..there was this one problem on the board, that was done last week. It had to do about the population in 'mathland'. Here's the gist of it. There are 25 million people in total; currently, 10 million of them live in the city, 8 million live in the suburbs, and 7 million live in the rural area.
This was also given:
    C           S          R
C [ 65% 31% 4% ]
S [ 18% 70% 12% ]
R [ 7% 8% 75% ]


I know how to do the transition matrix, but for some reason, I still don't know how to formulate the state matrix for these kinds of problems..BUT other than that, everything else is going okay. Well, that's my blog for this unit =)




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Todays scribe.

At the beginning of the class mr.k explained a lot more about blogging on blogging. he said that we should log on blogging on blogging to get the first question of the test. which will say that if you have blogged for the privous days, and the other benefit of logging on blogging is that you got to answer one question of the six given questions. then mr. k would know where students were facing difficulties and try to explain more to fill the holes on our brain. so no one would get less than 80% on the test. i think this where mr.k's dripping words of wisdom of todays class. then he gaves us notes as follows:


Matrix multiplication

Matrix multiplication is not like ordinary multiplication it's a little weird.

we multiply Rows and Columns in this manner: [ a b] [e f] [ae+bg af+bh]
[ c d] [g f]= [ce+dg cf+dh]

for example: [ 1 2] [5 6] [1*5+2*7 1*6+2*8] [19 22]
[3 4] [7 8]= [3*5+4*7 3*6+4*8]= [43 40]


Matrix Multiplication tips

(1) Not all matricies can be mulitplied, to check if they can be multiplied, do this:

step (1): write the dimensions side by side

step (2): if the inner numbers are the same they can be multiplied; otherwise they can
not. [3 4]
example: A= [1 2] B= [5 6]
A is A 1*2 matrix
B is A 2*2 matrix


could the following be multiplied?

A B BA
1*2 2*2 2*2 1*2
yes no
same inner dimensions different inner dimensions

(2) the solution matrix will have the dimensions of the outer numbers

(3) anther way to think about it:
matricies are multiplied "row by column" given AB=C the first row of A multiplied with the
first column of B. this gives the C,, Entry in the resultant matrix c.
(first row, first column Entry)

(4) unlike ordinary numbers matrix
maltiplication is not commutative.
in other word it is not always true that AB=BA

The Identity Matrix

Any matrix multiplied by I, the identity matrix, is unchanged.

I= [ 1 0 0 ...........0] I consist all Zeros and ones along its main diagonal
[010................0]
[0.......................]
[.. ...]
[00.....................]


Inverse Matricies

the "Inverse" of a matrix [A] is the matrix that when multiplied by A, gives the identity matrix.

the inverse of [A] is written: [A]^-1

Example: A= [1 3] B= [-5 3]
[2 5] [2 -1]

AB= [1 3] [-5 3] = [1 0]
[2 5] [2 -1] [0 1]

therefore [B] = [A]^-1 B is the inverse of A (and A is the Inverse of B).

important: matricies always commute with their inverses i.e [A] [A]^-1 = [A]^-1[A]= I

*not every matrix has an inverse

on the calculator: Entry matrix A then "call" it on the home screen. hit the [X^-1] button then {Enter} you will get matrix [A]^-1.

don't forget to check blogging on blogging.

this is all for today folks.







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Sunday, February 19, 2006 

Scribe

Im sorry i couldnt put this up earlier. For those of you that happened to miss Tuesdays class. Well here it is, its gonna be quite short tho because we really didnt do anything new.

So we started off that class by doing some review work on the connectivity matrix(Just so we didnt forget how it was done). A connectiviy matrix is a simple matrix that an airline company would use to keep track of their planes and flights. It gives them information about the possible routes from one city to another.

After doing that we did some more group work on transition matrices.

Nearing the end of the class Mr.K told us of a day that I had not knew existed. Yes and that is PIE day. Basically its a special day for eating pie. On the third month of the 14th day at 1:59 and 26 seconds it is supposively said thats the best time to eat PIE!. (3./14/15/1:59:26)

Well thats my scribe for today I have already chosen the next person for the scribe and I think he already posted his. (Remember dont forget to bring your pie on march the 14th :P)




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Chinese? Checkers? Chess?



Chinese Checkers it is called in England. Kinasjakk (Chinese Chess) in Norway. The truth is that it has nothing to do with neither checkers, chess, nor China.

'The Chinese Checkers game board is in the shape of a six pointed star and is playable with two up to six people at the same time. Each player uses pegs or markers of a different color placed within one of the points of the star. The object is to move all your ten pegs across the board (move one step at the time or jump over adjacent pegs) to occupy the star point directly opposite. The player getting all pegs across first wins.' - More.

You can play it here.

(Thanks again to Think Again!)




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Saturday, February 18, 2006 

Scribe

Our first project was assigned, and it's due on Monday, February 27th. We must hand it in at the beginning of class that day. We also got a sheet which must be handed in with the project. So if you missed class, see Mr. K on Monday to get it. There must be two signitures on it, one your own, and the other one of your parent's or a guardian. Mr. K will not accept the project otherwise.

The assignment conditions are that we're allowed to use any books, notes, a calculator, a graphing calculators, or a computer to guide us. Other than that, we're not to get any other kind of help. That said, we're allowed to work in groups of two, but no more than that. We may also ask Mr. K. We were advised to get the actual math part of the project completed over the weekend. That's 50% of the grade. We're allowed to see Mr. K on Monday to see that our math is correct. He believes that the minimum grade we should receive on this project is 88%.

As mentioned, the actual math is worth 50%. We may either get A (the student has correctly solved the problem, with few or no mechanical errors), B (the student has used the correct method, but has made a minor error in the use of mathematical techniques) , C (the student has found a partial solution to the problem), or D (the student has had little or no sucess in solving the problem) within that aspect of the project.

Communication is something else we're being graded on, and it's worth 30% of the project. In this part of the project, we may be given either E, H, S, or U. E for exceptional, H for highly satisfactory, S for satisfactory, and U for unsatisfactory.

Finally, we'll be graded on Presentation. That's worth 20%. We may be given E, H, S, or U.

Okay, so now you're ready to know.. dun dun dun.. the PROJECT.


Matrices - A Growing Community
Task A.
A powerful use of matrices is to describe and explore situations in which one state depends on a previous state. A transition matrix can neatly describe the transition from one state to the next.
Consider the growth of populations. Suppose that the people in a (fictitous) country can be divided into three groups; children (aged up to 12 years), youth (aged from 12 to 19), and adults (aged over 19). Suppose further that the following is known about the population of each.
  • 8% of the children become youths (because they get a year older)
  • 0.5% of the children die
  • 2% of the adults die
  • 12.5% of the youths become adults (because they get a year older)
  • 1% of the youths die
  • The number of babies born is 4% of the adult population

The number of people in each category in a particular year can be represented as 3 x 1. Matrix A= [c]
[y]
[a]

a) Formulate equations to represent the number of people the following year.
b) Summarise these relationships into a 3 x 3 transition matrix B

Enter the matrix B into your graphing calculator. To use the matrices to model the population change, you need to know what the initial population is. Suppose that c=250 000, y=150 000, a=500 000. Enter this information into the calculator as Matrix A, a 3x1 *column matrix.

*We're used to row matrices, keep that in mind while doing the multiplication (how we multiply)

With the above assumptions, the calculator will allow you to predict the next year's population as BA. It is best to start by evaluating BA; then find Mat B x Mat Ans.

c) What is the population predicted to be after one year? Describe the changes.
d) Repeat the command Mat B x Mat Ans and record the population for the next 14 years.
e) Comment on the distribution of the population over the 15 years.
f) Use a spreedsheet to table each category of the population over 50 years.
g) Graph the categories over this time.
h) Comment on the result and predict the future for the community.

TASK B 'Population Variations'
Investigate the long-term effect of the adult death rate rising from 2% per year to 4% per year.

Wow.. I wish I could say that I was almost done explaining what we did in class, but the fun's just beginning.

We had the pre-test. Then we got into our groups to correct. I suppose I could post the answers.. :P

1) Three stores, A, B, and C, were surveyed to determine costs of the same weight and brand of bread, flour, and sugar. The amounts to be purchased and the prices charged are shown in the matrices below. If all three items are purchased at the same store, what is the lowest total price?

Amounts ABC
bread flour sugar = [3 1 2]
Prices A B C
Bread [1.09 1.15 1.03 ]
Flour [6.15 5.95 6.45 ]
Sugar [4.32 4.30 4.10]

a) $11.40 b) 11.58 c) $17.74 d) $18.00 -- The answer is c. Just multiply Amounts matrix x Prices matrix.

2) A network matrix, N, shows direct routes between cities. Which matrix calculation determines the number of routes with exactly k stopovers between two cities in the network?

a) Nk -1 b) Nk c) Nk +1 d) Nk +2 -- The answer is C. I think a lot of people in the class got this one wrong. I honestly can't remember what the explanation was, my bad.

3) Determine (3Q)2 =
[-1 1]
[1 2] All it is, is using scalar multiplication 3 x the matrix, then squaring it. The result is

[18 9]
[9 45]

4) Solve for x:
[1 0] [x ]
[x 6] [0 3][-2] = 0 . First, do x times 1, then x times 0. That makes x. Then it's 6 times o, and 6 times 3. That makes 18. Hence, [x 18]. x times x makes x2. 18 x -2 makes -36. Now, because we have to make this equal zero, x can be -6 or 6.

5) A washing powder is sold in regular and large boxes. Market research shows that 40% of the buyers of the regular size switch to the large size for their next purchase, and 18% of the buyers of the large size switch to the regular size for their next purchase. The original market share was $70 for the regular size and 30% for the large size.

a) What is the market share for each size in the next round of purchases?
r l r l r l
[.70 .30] x r [.60 .40] = [.474 .526]
l [.18 .82]
This means that 47.4% is the next market share for regular powder, and 52.6 is the market share for large powder.

b) In the long term, what is the market share for each size of this washing powder?

For this, just do the same thing, except to the power of 50. :)

Wow, so close to being done.. yet so far. :P

The final thing we did (that I remember) was a group assignment regarding probability (next unit we're doing, by the way). Our test on matrices I believe is on Friday, or Wednesday. I can't remember if it's been settled ( sorry :( ).

Anyhow, the problem is as follows:

As we all know by now, our beloved Manitoba Moose are a team that is prong to streaky play. In other words, when they are winning, it seems like they will never lose again. On the other hand, there are times when they are losing and it seems like they will never win another game! Being the statistical sport that hockey is, Joe scoreboard (very lame :P) has made the following observations concerning the Moose. That is, when the Moose win a game, there is a 70% chance that they will win their next game. However, when the moose lose a game, they have only a 40% chance of winning their next game. Use this data to answer the following questions.

1. Write a transition matrix describing the situation above.

W L
T = W [.70 .30] The sum of each row must equal 1 (100%).
L [.40 .60]

2) Suppose that the moose won their first game of the season. What would the initial distribution (initial state) matrix?

D0[1 0] 1 represents that they won, while 0 represents that there is no chance they lost, because well, they won.

3) Given the conditions from 1 and 2, find the Moose's probable winning percentage after 1,2, 3, 4, 5, and 10 games. Mulitplythe matrix in question 2 by the one in number 1.

For example, Do10 = D0T10 ... What does D10 represent? ... For this one, I believe it means the number of games.

1) [.7 .3]
2) [.61 .39]
3) [.583 .417]
4) [.5759 .4251]
5) [.5725 .4275]
10) [.5714] [.4286]

Having played 10 games, could the Moose actually have a record represented by this posibility?
The answer is that they can't, because after 10 games you can't have won 57% of them.

4) Now, recalculate example 3 with the condition that the Moose lost their first game. Complete the chart below and compare the results. *To get the probabilities from having lost the first game, just change the state matrix from [1 0] to [0 1]

Winning percentage having won or lost first game.
W L
1 game .70 .4
2 games .61 .52
3 games .583 .556
4 games .5749 .5568
5 games .5725 .5700
10 games .5714 .5714

5) Notice that there is very little difference between the results after 5 games and after 10 games. What do these percentages represent?
These percentages represent the matrix stabilizing, meaning they can expect to win 57% of all the games they play.

7) The Moose play an 80 game regular season. Predict their final won-loss record assuming that they win their first game and also if they lose their first game. How do the records compare? In this example, how important is the initial state?

The records are the same, [.5714 .4286] .... This means that regardless of how their season begins, they may win 57% of all games they play. Therefore, the initial state doesn't really mean anything over time.


I am very sorry that it took me so long to post this (I also apologize for the length!). I hope I explained everything clearly and properly. Monday's scribe will be Mohamed.




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Well, it's nearly 3 am. Since I got home from work (after 1 some time), I've been typing out the post. I don't know if what I've got so far can be viewed as it's a draft, but a post is on its way in any case.. I just really, really need to go to bed.




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Friday, February 17, 2006 

I don't have time to do scribe post just yet. I have to leave for work shortly, but I should be able to do it after work.




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Thursday, February 16, 2006 

Scribe

Hi, Allan here. Today we just had the one class in the morning. The first part of the class we did practice problems on network and connectivity matrix. One of the problems asked for the fewest Relay Points. A relay point is a point that has to be passed to get to another. For example, if you have to get from A to C, and the only way to get there is through B, B would be the relay point.

After that, we got a small quiz about connectivity matrix. After the quiz Mr. K talked to us about the pre-test we'll have tomorrow. It'll have 5 questions on multiple choice, short, and long answers I think, but they will be similar to the test questions. After the pre-test we'll correct it in groups and hand in for marks. It's to prepare us for the test next Friday. With the test, he also reminded us about the first mark on our test that asks if we have posted. Read Blogging on Blogging if you haven't yet. He also talked about the movies on transition matrices he put up, and that we should always try those quizzes. Remember that we don't need to save our scores, the quizzes are there just to practice with.

About the end of class Mr. K showed how to turn a matrix into its inverse. You just put up a matrix and press the x^-1 key. Multiplying a matrix by its inverse should make an identity matrix.

Homework for tonight is the matrices and Codes worksheet, where you're encoding and decoding messages. There's a correction if you didn't catch it, in matrix [C] the -28 should be -27 on the third row third column.

I guess that's it,,, I know there's probably some stuff wrong or missing, so please comment!

Cait for tomorrows scribe.




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Wednesday, February 15, 2006 

Encrypting and Decrypting

Okay, for the 8 of us that showed up for class instead of excused skipping, mr. k had some fun lined up for us, and a sub-teacher. Matrices again but this time to decrypt and encrypt messages. First task was to figure out the teachers name, and that had a prize too, I won a sucker! lol then we, all 8 of us, combine our brain power to conqure the World assignment.

First to note is that there are two matrices labeled "Encrypt" and "Decrypt", note that when they are multiplied together they create an identity matrix. The message is changed character by character to number equvilants then those numbers were put into a 3x3 matrix and multiplied by the encrypting matrix to give us numbers used in the encrypted message. To get a readable message from the scrambled message you multiply by the decrypt matrix and change the numbers to their equvilants in the number-letter equivilant chart.


The Second class was a more interesting one with only 6 of us this time.... wierd how that worked out.... but with no more work for us to do Mr. K was called to assign us work. The Chapter 2.4 Review #1-9 which was fairly straight forward, but that probably only because i probably got some stuff wrong, i'll find out later though.... Laters :)




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Tuesday, February 14, 2006 

All About Matricies ....

This is an introduction to matricies.

You can review the basic operations (addition, subtration, scalar multiplication) on matricies here.

Learn about matrix multiplication there.

You can also watch two movies about Transition Matricies. (You might need to download the Quicktime Player; you can get it (free) here.) The first one explains the mechanics of what they are and how they work. The second movie takes you through two different examples, slowly and carefully, showing how to solve transition matrix problems. Something I haven't yet mentioned in class; transition matrix problems are also called Markov Chains. "Markov" is the name of a person.




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Monday, February 13, 2006 

Transition Matrices

Hey, My apologizes for posting up so late!

But let's just get to the point. For today we had two periods of math, but in the morning class we were told that we were going to have an assembly. So that pretty much took up the whole morning class to learn anything. But Mr. Kuropatwa did give us a little chit chat on whats up with the blog. Like how he posted a puzzle/game yesterday and how it may also be math related. Mr. Kuropatwa will be doing this on every Sunday for now on. So be sure to check them out!

He also mentioned that he will be planning to set up a little chat box so that if we need help with anything we can ask questions and of course we can chat with each other?! Hopefully! But like what Mr. Kurapatwa said don't mention your name, your location, your school, or any kind of information that can give you away. So if you haven't read "Students Made This!", I advise you to do so. It talks about everything you should know when being online. It's pretty helpful I say.

As for our second class, we learned the last type of matrix in this unit. TRANSITION MATRICES.

Transition Matrix: a square matrix that shows how the probability of one event is dependent on the probability of another event occurring.

For example, in class we did this one example with sports. I know you guys probably have the notes on this already but for the ones who missed today's class but maybe if I explain it might help or not? I'll give it a shot.

Sports
The annual Oxford-Cambridge boat race, has been rowed regularly since 1839. Using the date from 1839 up to 1982, there were 58 Oxford wins and 67 Cambridge wins. If the relationship between the results of a given year and the results of the previous year are considered, the following table can be constructed:

To
O C
From Oxford [35 22 ]
Cambridge [23 44 ]

So now the question askes us (a) to convert the "number of wins" to percentages to rewrite the above matrix.

So what we do is each score and divide it by the total of races.

[35/57 22/57]
[23/67 44/67]

We get 57 and 67 by adding each of the rows.

We then get this [.614 .3859]
[.3432 .6567]

(b) If Oxford wins this year, what is the probability they will win next year? In two years? Three?
So then to get to this solution we will take our STATE MATRIX which is [1 0] because it represents 1 for Oxford wins and 0 for Oxford loses. We take that and multiply it with our TRANSITION MATRIX which is our matrix up there where we figured our our percentages.

[1 0]x[.614 .3859]
[.3432 .6567] = [.614 .386]

In the resultant matrix in A11 it represents the percentage that Oxford wins. And in A12 that represents the percentage that Oxford loses.

And if you want to find out for the next year all you have to do is take the resultant matrix [.614 .386] and multiply it with our transition matrix.

[.614 .386]x[.614 .3859] =for the next year.
[.3432 .6567]

And if you want to find out for long term to see what percentages of games will Oxford win. All you have to do is take our state matrix with was [1 0] and multiply it with our transition matrix to the exponent of how ever much what to see it. Like say if you want to see if Oxford would still be winning after 10 years you'll just multiply it to the exponent of 10.

[1 0 ]x [.614 .3859] ^10=
[.3432 .6567]

Yeah, so I'm not to sure about this, but I tried...at least. So sorry guys!

Uhm, tomorrow's scribe will be....Dom.

G'night!




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Sunday, February 12, 2006 

Sunday Funday!

Each Sunday, just for fun, I will post an online game or puzzle. This week it's a logic puzzle ... we look in on a prisoner with a problem ....




For the last trial, the king used not two, nor three, but nine rooms! The prisoner was told that one room contained a Lady and the other eight were either empty or filled with a tiger. The sign on the Lady's door was true, the signs on room with tigers were false, and empty rooms had signs that were either true or false.

These were the signs:

  1. The lady is in an odd-numbered room.

  2. This room is empty.

  3. Either sign 5 is right or sign 7 is wrong.

  4. Sign 1 is wrong.

  5. Either sign 2 or sign 4 is right.

  6. Sign 3 is wrong.

  7. 7. The lady is not in room 1.

  8. This room contains a tiger and room 9 is empty.

  9. This room contains a tiger and 6 is wrong.


The prisoner studied the nine signs for a while and came to the conclusion that the problem was unsolvable. The king admitted his mistake and told the poor prisoner if room eight was empty or not.

The prisoner needed no more help. He deduced where the Lady was. What about you?

Problem source: The Lady or the Tiger and other Logic Puzzles by Raymond Smullyan. (With thanks to Think Again!)




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Saturday, February 11, 2006 

Eyy...everyone.....Ivy would like to tell all the 40s Applied Math student... what happened or what she've learned today....

We only have one class...but sure do my brain almost explode in what we have for the group problem...but anywaysss...

Mr. K gave us some matricies question.. about connectivity matrix at the first part of our class....yesterday i was pretty confused about it.. but i finally got it when Shane actually explain it to me...Second part is about our text book assignment...Mr. K asked us about any problems we encounter by doing the textbook questions...and so he explained some problems that we didn't get.


The Group Problem
WE did this problem about 6 guys doing the activity of ski jump. It has the number of points that those guys got and the difficulties. The question is....how can we explain by multiplying the points and the difficulties by making a matrix model; also to find who got the greatest points and the least. How can we do that?

Guy 1 - 24.3 27.5 27.1 21.4
Guy 2 - 21.2 24.2 18.3 15.2
Guy 3 - 21.3 21.8 15.9 21.5
Guy 4 - 18.7 27.2 21 18.6
Guy 5 - 24.4 24.2 21.4 24.5
Guy 6 - 27.6 18.3 21.6 21.5

^ What you See on top is the ski-jumpers points.^

I 1.4 1.5 1.3 1.6 1.5 1.2
II 1.6 1.4 1.7 1.4 1.6 1.5
III 1.5 1.9 1.9 2.0 1.9 1.7
IV 1.7 2.1 1.4 1.8 2.0 1.9

^ What you See on top is the Ski-jumpers difficulties.^

It's also asking us which way is the better idea to multiply the points and difficulties. Lets give a names to this two data of the ski-jumpers.in matricies.. Let be Points = A and Difficulties = B. So which way is better?


[A] is (6x4)
[B] is (4x6)
THEY CAN BE SOLVE IN BOTH WAYS. butttttttt........which is the right one????


SOLUTION
Lets put it this way [a] x [b] = THE PRODUCT. So if [A] got rows and columns by 6x4 and [B] got 4x6 it can be solve...and our product should have 6x6 in rows and columns. We are solving it this way because we need to find all the total points for each ski-jumpers and it's possible to do this way, yes they do have different types of difficulties in each jumpers but in order to be fair we need to multiply them with the different numbers of the other ski-jumpers. NOW if we got all the product by multiplying [A] x [B] in matrix..thenn...to add up all the total points of the ski-jumpers we need to multiply the product with "1" that has 6x1 rows and columns...

We don't add the following individualy because it's going to take time, by multiplying with "1" in 6x1 we should have the ski-jumpers total...and see who got the most points and least.

<<------------------------->>


[A] x [B] = THE PRODUCT
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]

[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]


<<-------------------------->>


AND THAT'S THE CASE!!! HOPE I DIDN"T CONFUSE YOU........

Monday's Scribe (Feb. 13, 2006) is going to be : Corrie.
I'm sorry for the person that i chose... i barely know everyone in this class...




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Thursday, February 09, 2006 

SCRIBE

Hi everyone =)

This is Steph, and this is what we did in class today..

To start things off we had a quiz -_- I hope everyone did good! While we were correcting the quizzes, Mr. Kuropatwa started talking about the provincial exams and showed us how they would be marking. It's very important that you don't leave out any intermediary steps; meaning you should be showing all of your work. If you don't, 1/2 marks will be taken off!! So everyone should get into the habit of doing that. After the quiz we recapped what we knew about matricies by doing some problems on the board.

Today we learned about connectivity matrices. From what I understand it deals with finding how many ways possible to go from one place to another by using the data from a matrix. Matrices can be used to summarize the routes between cities and to even calculate the different number of routes. These matrices are used to solve network problems.
Example:
The bus navigator on the internet uses matrices.

It's also useful to make a network diagram. A network diagram is used to build the initial connectivity matrix. Using a map gets confusing very fast. So instead you use a network diagram by making matrices. Take the assignment we did in class as an example; when you take the initial matrix and raise it to a power, it will determine the number of flights you will take. (You use your calculator for this).

Example: initial matrix
[ 0 1 0 ]
[ 1 0 1 ]
[ 0 1 0 ]

initial matrix to the power of 4
[ 0 1 0 ]^4 [ 2 0 2 ]
[ 1 0 1 ] = [ 0 4 0 ]
[ 0 1 0 ] [ 2 0 2 ]

After the assignment we worked on a group problem about animals having restrictions on sitting next to eachother :p

At the end of class Mr. K handed out our textbooks *yaaay* so we could finally do some homework.
If you haven't already finished page 55 - 59 ; questions 1 - 9, definitely finish that.
We also have page 64 - 67 ; ODD numbers only.
And our homework for tonight is on page 76 - 79 ; questions 1 - 7.

Tomorrow's scribe will be: Ivy.




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Wednesday, February 08, 2006 

The Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post is can be quickly accesed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

Cycle 4
Cait
Shane
Allan
Ivy
Nikki
Steph
Nik # 1/2
Corrie
jessica
jason
Dominator
mohamed
khan
Andrew
Pa3k
reign
Hesy
muuxi
Rubie




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Scribe

Hey what's going on,

It's Jason, today's going to have a really short scribe entry because we only had one period of math instead of two.

Anyways all we did was work on the questions we got from the text book yesterday or the day before. I can't remember when we were assigned them. ( page 55 questions 1 - 9 for those who forgot)

And for those who finished those questions questions on page 64 were assigned. Were suposted to do questions 1 - 9, but only do the ODD numbered questions. ( 3, 5, 7, and 9)

The last thing we ended up class with was Mr. K started to talk about identity elements, but he said he plans go into greater details about them in a later class. The definition the math dictionary ( is a link on the blog) gives of identity is kind of confusing so I'll just explain the basics of it myself. ( if it makes absolutely no sense check the math dictionary)

A identity element/equation is basically something you do to one number to get the same number. I know its really hard to explain.

Example

-The indentity element for addition is 0. No matter what number you add zero to you get the same number
Ex: 1 + 0 = 1 or 27483 + 0 = 27483

-The indentity element for subtraction is the same as addition, 0.
Ex: 2 - 0 = 2 or 323 - 0 = 323

-The indentity element for multiplication and division is 1.
Ex: 7 x 3 = 21 or 74232 x 1 = 74232
4 /1 = 4 or 637/1 = 637

- The identity element for a square matrix is having nothing but ones going diagonally and zeros in all the other squares.
Ex:

1 0 0
0 1 0
0 0 1

or

1 0
0 1

If you don't get it well probally go over it in class again sometime. The basics of it is very simple.

Well that all we did cya

tomorrows scribe is: Steph




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Compare, Contrast.

One similarity that I can think of at the moment for scalar multiplication, matrix multiplication, and normal multiplication is that you may multiply them in any order and the product will be the same, for matrix multiplication this is if the matricies in question are the same. I believe that's how it is in the case of matrix multiplication, anyway. :P I'm confusing myself trying to explain this. :P

The differences between the three is that while it doesn't matter with scalar multiplication and normal multiplication in any case, when matricies are not the same, if placed in a different order, the product will be different. Another difference is that with matrix multiplication, there's the funky process where it's A11 x B11 + A12 x B21 ... A being the first Matrix and B being the second. 11 being the first row and first column, 12 being the first row and second column, and 21 being the second row and first column. Then you do A11 x B12 + A12 x B22, etc, etc, etc.

That's all my head will allow me to produce without it imploding, I hope I've got it right.

As for the two 2 by 2's that produce the same resultant matrix:

Matrix A = 33 55 Matrix B = 33 55 Matrix C = 2424 4040
Matrix A = 12 21 Matrix B = 12 21 Matrix C = 54 45




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Tuesday, February 07, 2006 

Commutative Law :)

Hello there this is my post on the similarities and differences of mulitplying numbers and multiplying matricies!

The things that are the same about multiplying matricies and numbers is that you can multiply it 3x2 or 2x3 in both cases as long as the matricies are good and are not undefined, like the matricies must have dimensions where the two middle numbers are the same like if matrix A=3x2 and matrix B=2x3 and in this case the two matricies can commute wih each other.

The difference is that it doesnt matter which way you multiply numbers they will most likely be the same all of the time, now if you multiply a matrix where A=2x2 and B=3x2 it won't happen becuase it will come out undefined.

The commutative law says that it doesnt matter which way you x/+ by because it will always end up the same but it matters on which way you divide and subtract by because if you divide 3/2 and then swith it to 2/3 the answer will be different.

Example: A= 2 4 B= 2 4
6 8 6 8

Answer= If AxB= 28 40 If BxA= 28 40
60 88 60 88

You must multiply these matricies, and don't forget to usae your hands to count the ways or numbers, and that is the end of my assignment have a good day.:)

(* Remember to put square brackets around the matricies, unfortunatly i cant do that right now.)

Nicole




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Scribe!!!!

Hey All,

It's Nik. Anyways here's what happened today in Class:

Dictionary Additions:

Types of Matrices
Rectangular Matrices: Have different numbers of rows and columns

EG. [6 6 7]
[5 2 9]

Square Matrices: Have the same number of rows and columns.

eg. [4 5]
[7 2]

Row Matrices: have only on row

EG. [7 5 3 2 9]

Column Matrices: have only one column
Eg.
[6]
[5]
[2]
[9]
[5]

Multiplication by a scalar:

To multiply a matrix by a scalar quantity, we simply multiply each elemt by the scalar.

Eg.

5 [1 2] = [5 10]
[3 4] [15 20]

REMEMBER: Rows go across, columns go up and down.

Non- Dictionary Stuff:

How to use your Graphing Calculator For matrix activities:

For TI-83
Hit the Matrix Button,
Scroll across at the top of the screen to Edit,
Plug in the dimensions (# enter # Enter),
Plug in your elements,
Name your Matrix (A-J)
you can now do operations by going all the way to the left on the top of the screen.
Eg: A + B will add matrix A and Matrix B,
to store a matrix, hit the store button.
you will get: ANS --> (designate an unused matrix)

Other things to know:

for this class, you should have 12 PENCILS! you may not hand in anything done in pen! keep two pencils in your binder, and ten more in your locker, YOU WILL NEED THEM THROUGH THE COURSE!

Commutative law: Basically, the statement that it matters in what order you subtract and divide numbers, but not what order you add and multiply.

We also learned about multiplying matrices, but that will be for tomorrows scribe as we have yet to take any dictionary notes.

Tomorrows scribe is: Jason




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The Matrix: Part I

So far in class we've learned how to add and subtract matricies, how to multiply maticies by a scalar quantity and how to multiply matricies.

Matricies are usually used to solve "systems of equations" like you did in Applied Math 30S. We wont really be using them in that way in this course but you can read about it here. It may be worth your time to review that link if you'd like to go over the definition of what a matrix is. You may also want to look it up in the Math Dictionary or Encyclopedia you'll find in the Links list over there --> in the right hand sidebar.

You'll find a review of our lesson on Matrix Addidition here and Matrix Multiplication there. (There's a cool animation -- you'll see what I meant about "using your fingers." ;-))

Find a little addtional Matrix Addition practice here, and Matrix Multiplication practice there.

Finally, test your knowledge with these online interactive quizzes (refresh the page if you want to try five new ones):



Remember, those quizzes are tonight's homework.

Cheers!
Mr. K.




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Blogging on Blogging

We had a good couple of classes today. I was very happy with how well you seem to be, as a class, learning and applying the material but there's one thing that concerns me. Do you remember my "zoned out minute?" Well, at that point I was feeling as though you were all there in body but not in spirit. What I mean by that is there is a BIG difference between learning and just being there. Learning is an interactive sport; not a spectator sport. There has to be a conversation between us, back and forth, as we work through the material. Learning doesn't happen when I talk and you listen; learning happens when you have a conversation -- with me and with each other. I'm looking forward to participating in more conversations in our future classes, then, maybe, I wont zone out. ;-)

We were talking about exactly what sort of post you're supposed to make to get that mark on your test. The kind of post I'd like you to make should have one or more of these characteristics:

  • A reflection on a particular class (like the first paragraph above).

  • A reflective comment on your progress in the course.

  • A comment on something that you've learned that you thought was "cool".

  • A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.

  • Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.

  • Respond to a Blogging Prompt I posted. (see below)


Your posts do not have to be long. I'm far more interested in the quality of what you write rather than the quantity.

Blogging Prompt
To help us along our blogging journey I've decided that I will also occasionally post a Blogging Prompt. It will be easy to find because I'll always put it under a heading like the one above this paragraph. Feel free to create your own Blogging Prompt for the rest of us if you like. If it's a really good one (i.e. has rich possibilities for blogging) we'll count it as your post. ;-) Here's my first one:

We've learned about two different kinds of mutliplication that can be done with matricies; scalar multiplication and matrix multiplication. There's also ordinary multiplication, such as 2 x 3 = 6. Blog a brief paragraph identifying ways in which these three types of multiplication are similar. Blog a second paragraph outlining the ways in which they are different. Also, give us an example of two 2x2 matricies, A and B, that DO commute. i.e. AB = BA.


This sort of compare and contrast exercise can be made easier to do using Venn Diagrams. Draw two large overlapping circles. List the similarities in the overlapping section and the differences in the appropriate non-overlapping sections. If you like, you can use this web tool to do it online. If you do blog about this prompt and want to post your diagram we'll talk about how to post pictures sometime in class. ;-)

Happy Blogging!




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Monday, February 06, 2006 

SCRIBE!!!!!

Hello well this one is going to be shorter and simpler cause i did a really really long one and it went missing so yeah sorry for the confusion but it is I Nicole blogging and informing those of you who missed today or need some more info on wat we did today. This is for the 40s Applied Math class by the way :) Today is DAY 1 Feb.6/06

1. Ethics
2.Scribe
3.Matricies

We had an introduction to what we will be doing on the internet, like blogging and emailing and reading and all tat jazz, so yeah and u must check out the site daily because it is part of the
6 steps of remembering that i will talk about in a bit.

We learned about what scribes must do and that is what i am doing right now which wil be updating you on and anyone else on what we learned in class and what not, oh and everyone gets a chance to do this job so enjoy everybody:)

We filled out a Student Information Sheet for Mr.K which will help him learn a bit more about each of us and stuff and he can learn about our dislikes and likes!:) WAHOOO

Oh and we cant forget that the blogs we had to submit last Friday are or were do today, and for those of us who werent there last Friday we have a chance and our blogs must be in by tomorrow so dont forget about that EH!!!

We learned about 6 ways in whcih we can remember our work that we learned today and every other day that we did work and here they are:

- 1st step to remembering will be when we are listening to Mr.K talk about what we wil be doing.

-2nd step will be when we are writting down what Mr.K is talking about.

-3rd step will be when you go home and check out the daily scribe blog which will contain what we have learned or our lesson for that day.

-4th step will be up to you, because you must call a friend or chill with a friend from your class and just briefly go over what you did in class, like talk about it ! :)

-5th step will also be up to you, actually entirely becuase it is a time to be responsible, so at least once during your free time take another minute and look over your notes and do it just because.

-6th step will be before you go to sleep or something, you will take out your notes and just read them again and then go to sleep.

Follow these steps and you shouldnt have trouble remembering, and it is critical you do this cause the very next day of class you or we will be learning something entirely different so be prepared:) !!!!

Mr.K gave us a little Pep talk about what we whould not put on the internet on any site which requests a picture or last name. These rules are mentioned at the beginning of the blog site but i'm goin to tell you agian: NO PICTURES OF YOURSELF-if you want a pic. put one of something that defines you or something like that and NO pics. of family members. NO LAST NAMES :)

Here is todays lesson all writtin out for you, just for you!!!!

Matrix: A table of numbers arranged in rows and columns conrtined(?) in square brackets. The plural of Matrix is Matricies. They are usually named using capital letters.

Example:A= [1234]- this is a matrix row which is one of the many different types of matricies.

Dimensions of a Matrix: Determined by the number of rows and columns.

Written as: r x c Expressed as: "r by c"

Example: Matrix A is a 3 by 4 (3x4) Matrix

Element of a Matrix (AKA entry)
-one of the values of a Matrix
-The "address" of each value is expressed by its row and column position.

Example: A23 = 6 [read as:"a-two-three"]
The element in the 2nd row, 3rd column of Matrix A is 6.
A=Element in Matrix A 2=Row 3=Column

This is what we learned in class today and what we must write down in out Dictionaries (our little Hilroy book :) ).

Our dictionary is our book that is worth 10% of our mark so dont forget to write in it everytime we are asked and keep it nice and tidy all of the time, meaning no doodleing on the cover :)

This is the end of the Scribe or my scribe and for tomorrows i choose the boy NICKY AKA Nick have fun and have a good day :)




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Students Made This!

Blogging is a very public activity. Anything that gets posted on the internet stays there. Forever. Deleting a post simply removes it from the blog it was posted to. Copies of the post may exist scattered all over the internet. I have come across posts from my students on blogs as far away as Sweden! That is why we are being so careful to respect your privacy and using first names only. We do not use pictures of ourselves. If you really want a graphic image associated with your posting use an avatar -- a picture of something that represents you but IS NOT of you.

Two teachers in the U.S.A. worked with their classes last year to come up with a list of guidelines for student bloggers.

One of them, Bud The Teacher, has these suggestions, among others:

  1. Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.


  2. Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.


  3. Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.


  4. Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.


Another teacher, Steve, developed a set of guidelines in consultation with his students. You can read them here.

Look over the guidelines and add the ones you like in the comments section below this post; either from one of Steve's students or one of your own. I think Bud's suggestions are excellent. We'll be using the one's I highlighted above as a basis for how we will use our blog.

Cheers,
Mr. K.




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Saturday, February 04, 2006 

Graphing Calculator

Okay, so I don't know about the rest of the people in this class, but I sure didn't have a graphing calculator.

I went to Staples today, and picked myself up a TI-83+ ($128.76). I would've gone with the Casio FX-9750Plus ($79.99), or even the Staples BD-6120G ($34.99), but personally I'm used to the TI-83. I've been using it for Math since some time in Grade 10. Also, there are higher versions of the TI, 84 (84 silver aswell) and 89.

I can't really think of another place to look for a graphing calculator, except perhaps Grand and Toy.

All and all, I'd say if you can borrow a graphing calculator from someone for class, do so.




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Friday, February 03, 2006 

You're Here! Let's Begin ...

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (here's the course outline); for parents to find out "How Was School Today;" to share your knowledge with other students;.... Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, or make your own blog and link it to this one, or....the sky's the limit...let your imagination soar and lets get down to some serious blogging!

Here's your first online assignment:

Do you see the Links list in the side bar over there on the right? Follow the Study Skills Resources link. Browse through the sites until you find one that you think has excellent suggestions on how to study math; then, on a piece of loose leaf paper (or this worksheet) to be handed in on Monday:

  1. Write the address and name of the site you most liked.

  2. Rate the site out of 100; i.e. give it a grade!

  3. Write a brief description (no more than 4 or 5 sentences) of the site.

  4. Include a comment on what it was about this site that made it stand out for you (no more than 1 or 2 sentences).


Repeat this exercise for the second link that deals with Test Taking, i.e. how to write a test.

If you take this assignment seriously now and invest some real time and energy into it, you'll probably do real well in my class this semester...who knows, it might even help you in your other classes too! ;-)

Have Fun!

PS Don't forget to email me ASAP and get signed up as a contributor to our blog!! When you get your "invitation" to our blog, follow these directions to get yourself signed up at Blogger.




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