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On this page we hope to clear up problems that you might have with
matrices. Matrices are good things to have under control and
know how to deal with, because you will use them extensively in
pre-calculus to solve systems of equations that have variables up
the wazoo! (Like one we remember with seven equations in seven variables.)
Multiplication Quiz on Matrices
To add matrices, we add the corresponding members. The matrices have to have the same dimensions. Example: _ _ _ _
1. Problem: | -5 0 | | 6 -3 |
| | + | |
|_ 4 1 _| |_2 3_|
Solution: Add the corresponding members.
_ _
| (-5 + 6) (0 - 3) |
| |
|_( 4 + 2) (1 + 3)_|
_ _
| 1 -3 |
| |
|_6 4_|
Subtraction of matrices is done in the same manner as addition.
Always be aware of the negative signs and remember that
a double negative is a positive!
You can multiply a matrix by another matrix or by a number. When you multiply a matrix by a number, multiply each member of the matrix by the number. To multiply a matrix by a matrix, the first matrix has to have the same number of columns as the rows in the second matrix. Examples:
_ _
1. Problem: | -3 0 |
3| |
|_ 4 5_|
Solution: Multiply each member of the
matrix by 3.
_ _
| -9 0 |
| |
|_ 12 15 _|
2. Problem: Multiply the matrices shown
below.
_ _ _ _
| -2 1 || x |
| || |
|_ 4 -1 _||_ y _|
Solution: Multiply the first member of each
row in the first matrix by the
top member of the column in the
second matrix. Multiply the
second members of the rows by the
bottom member of the second matrix.
_ _
| -2x y |
| |
|_ 4x -y _|
Take the Quiz on matrices. (Very useful to review or to see if you've really got this topic down.) Do it! |
