Multiplying Matrices Tutorial

(Easy simple instructions)

By: Yuka Eguchi

 

-----------------------------------------------------

Before you learn how to multiply, you need to know what dimensions are:

The product matrix's dimensions are
(rows of first matrix) ~ (columns of the second matrix )

Example:

 

 

 

 

2

3

 

 

 

 

 

 

The dimension for the matrix above is 1x2

--------Practice-------

 

1.

 

 

 

 

5     7     6

4      5     2

 

 

 

 

 

 

2.

 

 

 

 

8   9

2    4

6    7

12   0

 

 

 

 

 

 

----------------------Multiplying Maxtrices-----------------------------

A. Find the solution for AB:

 

 

 

 

1 0 2

1 5 0

 

 

 

 

 

 

 

  -1  -3

4   2

-7  5

 

 

 

 

 

 

                                                                   A       x       B

Step 1: Multiply the corresponding entries in the first row of A and the first column of B. In other words, you would take the first row of A and the first column of B, and multiply the first entries(1 and -1), then the second entries(0 and 4), then the third(2 and -7) and add them up.

 

 

 

 

(1)(-1)+(0)(4)+(2)(7)        (1)(-3)+(0)(2)+(2)(5)

(1)(-1)+(5)(4)+(0)(7)             (1)(-3)+(5)(2)+(0)(5)

 

 

 

 

 

 

So your solution would be:

 

 

 

 

13    7

19   3

 

 

 

 

 

 

 

NNNNNNNNNNNNNNIMPORTANTNNNNNNNNNNNNNN

You can multiply two matrices if, and only if, the number of columns in the first matrix equals the number of rows in the second matrix. Otherwise, the product of two matrices is undefined.

Ex:

            

 

 

 

 

1

2

 

 

 

 

 

 

 

1  3   8

9  5   1

10  4  3

5   6   4

 

 

 

 

 

 

     1x2          3x4                      

The matrix above is undefined because the middle numbers of the dimension(2 and 3) are not the same.

======================================================================

Also, remember that AxB is not the same as BxA. For example, say you have AB with the dimensions of (matrix A)2x3 and (matrix B)2x2.If you were to multiply them as AB, it wouldn't be possible-but if you were to switch their order so it becomes 2x2 and 2x3. However, you cannot do this! If the question tells you to find what AB is-then you have to solve it as AB. You cannot switch the orders!!!!

----------------------------------------        Practice   -----------------------------------------

 1.

 

 

 

 

3   9

2   0

 

 

 

 

 

 

0  5    5

9  10  2

 

 

 

 

 

2.

 

 

 

 

1    4

6   -2

 

 

 

 

 

 

 

 

 

2    2

8   -1

 

 

 

 

 

 

5   1

0    0

 

 

 

 

 

 

 

 

 

3    

 

 

 

 

5    8   2

1   -6  0

2     1  5

 

 

 

 

 

 

 

0  4

3   2

1   7