# 2.5.1 Multiplication of Two Matrices (Examples)

Example 1:
Find the product of the following pairs of matrices.

Solution:

(b)

(c)

(d)

(e)

Example 2:
Find the values of m and n in each of the following matrix equations.

Solution:

$\begin{array}{l}\text{(b)}\\ \left(\begin{array}{cc}m& 2\\ -3& 1\end{array}\right)\left(\begin{array}{l}2\\ n\end{array}\right)=\left(\begin{array}{l}12\\ 4+2n\end{array}\right)\\ \left(\begin{array}{l}2m+2n\\ -6+n\end{array}\right)=\left(\begin{array}{l}12\\ 4+2n\end{array}\right)\\ -6+n=4+2n\\ n=-10\\ 2m+2n=12\\ 2m+2\left(-10\right)=12\\ 2m-20=12\\ 2m=32\\ m=16\end{array}$

$\begin{array}{l}\text{(c)}\\ \left(\begin{array}{cc}m& -3\\ -1& 1\end{array}\right)\left(\begin{array}{cc}-1& 2\\ 4& n\end{array}\right)=\left(\begin{array}{cc}-14& -11\\ 5& 3\end{array}\right)\\ \left(\begin{array}{cc}-m+\left(-12\right)& 2m+\left(-3n\right)\\ 1+4& -2+n\end{array}\right)=\left(\begin{array}{cc}-14& -11\\ 5& 3\end{array}\right)\\ -m-12=-14\\ -m=-2\\ m=2\\ -2+n=3\\ n=5\end{array}$