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.

Example:
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] = 2x3 ('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