Sunday, February 11, 2007

Matrix Operations

Hey and Hello,
In class today we were introduced to Matrix Operations. We learned four ways; Matrix Addition, Matrix Subtraction, Scalar Multiplication and Matrix Multiplication/Two-Finger Method.

Matrix Addition

IS commutative.*
Rule: Matrix Addition is only possible when the rows and columns are the same dimensions in A + B. Meaning that if you try and add a 2x3 matrices with a 3x1 matrices, you will get an error.
ie. [3 2 1] + [5 6 7] - will work.
[4 1] + [4 9 8 2] - will not work.

Matrix Subtraction

NOT commutative.*
Done the same way as Matrix Addition, rule still applies.

Scalar Multiplication
"Scalar" refers to the number you place in front of the matrices you are multiplying it by.
ie. 2[A]+[B]
'2' is the scalar quantity.
Scalar multiplication is done the same way as Matrix Multiplication except you add a number(s) into your equation.

The following matrix represents the amount Carol gets paid for doing chores for her parents. She gets $1.00 for sweeping, $2.00 for washing the dishes and $3.00 for folding clothes.

If carol does each of these chores for 2 weeks, how much will she make in each category?

To solve this problem you would enter these numbers in matrix A. Than clear your screen, put in 14, than press 2nd, x-1, than select [A] and press enter. This should bring you back to the home screen where you should see 14[A]. Press enter and it will give you an answer of [14 28 42]

Therefore, Carol will make $14.00 for sweeping, $28.00 for washing the dishes and $42.00 for folding clothes during a two week period.

Matrix Multiplication
NOT commutative.*
Rule: In order to multiply two matrices by one another, the number of columns in the first matrix must be the same as the number of rows in the second matrix.

This WILL work:

[A] = 2x
3 ('2' represents the # of rows, '3' represents the # of columns.)
[B] =
3x4 ('3' represents the # of rows, '4' represents the # of columns.)

This will NOT work:

[A] = 2x4
[B] = 1x2

Two Finger Method
This method is done by giving a 'thumbs up' with your left hand, than extending your index finger, while your right hand shapes the letter L. With your hands in position, follow a pattern like this:

If done correctly, you should get a final answer of
[17 9]
[27 -17]

And that my friends is it! Have a good weekend =)

Homework - Due Monday
Exercise #2; Page A-5, #2
Exercise #2; Page A-7, #6 & 7

Need More Help?
Matrix Multiplication/Finger Method
Matrix Addition & Multiplication
Matrix Addition & Scalar Multiplication

*Commutative: the ability to changer order


Ryan Maksymchuk said...

Marsha, fantastic stuff you've left here. I'm not sure if your classmates know how lucky they are to have you scribing and leading the way. As usual, I really appreciate your efforts, and I find myself really looking forward to what you may submit to the blog. Great stuff!!, and on behalf of your peers, thank you...

Ryan Maksymchuk said...

On another more practical note, I'm curious about the technical side of posting the pictures for your examples...they're great! Did you create them? or download them? Maybe you can share in class...Thanks again, Marsha.

Mr. Kuropatwa said...

Hi Marsha,

This scribe post is fantastic! The graphics are outstanding ... I particularly liked the ones where you illustrate both the correct and wrong way to do matrix multiplication. The green check mark and red X are really effective in getting your point across.

I also teach this course at a high school in Winnipeg and I'm going to link to your post from our class blog for all the students in my class.

A really beautiful scribe post. You've set the bar quite high for the scribes that follow you. Bravo!!

Darren Kuropatwa
Dept. Head Mathematics
Daniel McIntyre Collegiate Institute

Mr. Kuropatwa said...

... and BTW, the links to external sites for additional help were great!