Algebra II: Matrices

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.)

Addition and subtraction
Multiplication
Quiz on matrices

Addition and Subtraction of 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!

Multiplication of Matrices

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. The quiz is very useful for either review or to see if you've really got the topic down.

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