### 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.

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]

(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.

*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.

Page 89... Questions 1 through 5 ;)

Posted by Cait | 2/20/2006 7:36 PM

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