Multiplying Two Matrices

**Matrix Multiplication**

Multiplying Two Matrices

To find the product of two matrices, such as matrix

*M*and*N*, we need to look at the first row for matrix*M*and the first column for matrix*N*.Once you find them, multiply corresponding elements, and find the sum of their products.

(1 7) + (2 9) + (3 11) = 59

__This is the first element of the resultant matrix.__

Now locate the first row for matrix

*M*and the second column for matrix*N*. How can you find the second element for the resultant matrix?Once you find them, multiply corresponding elements, and find the sum of their products.

(1 8) + (2 10) + (3 12) = 64

__This is the second element of the resultant matrix.__

For the next step we are going to repeat the same procedure, but this time we will work with the second row of

*M*and the first column of*N*, followed by locating the second row of*M*and second column of*N,*and we obtain(4 7) + (5 9) + (6 11) = 132

__This is the third element of the resultant matrix.__

and

(4 8) + (5 10) + (6 12) = 154

__This is the fourth element of the resultant matrix.__

Therefore, the resultant matrix is

Can These Matrices Be Multiplied Together?

If

*M*is an*x**y*matrix,and*N*is a*y**z*matrix, the product of*M***N*is an*x**z*matrix. To determine whether or not matrix*M*and*N*can be multiplied we need to look at the size of each matrix. Since*M*is an*x**y*and*N*is a*y**z*matrices,*y*needs to be in the same in order to be a multipliable matrix. Also*x*and*z*will determine the size of the resultant. Therefore*M**

*N*=

*MN*

*x*

*y * y*

*z*=

*x*

*z*

__Equal Order of__

*MN*So, if matrix

*M*is 3 4 and matrix*N*is a 4 2, then*M***N**is possible since 4 = 4, and the size of the resultant matrix is 3 2**.*

*N**

*M*

*is not possible since 2 3.*

It is important to know that if

Multiply if possible.

1)

2)

3)

4)

1)

2)

3) Not possible

4)

*M***N**is possible, it does not mean that**N***M**is possible as well.***Practice**Multiply if possible.

1)

2)

3)

4)

**Answers**1)

2)

3) Not possible

4)