# Addition and Subtraction on Matrices (Sample Questions)

Example 1:
Find the addition of the following matrices.

Solution:

Example 2:

Find the subtraction of the following matrices.
$\begin{array}{l}\left(a\right)\text{}\left(\begin{array}{l}9\\ 6\end{array}\right)-\left(\begin{array}{l}7\\ -2\end{array}\right)\\ \left(b\right)\text{}\left(\begin{array}{cc}3& -4\\ 0& 5\end{array}\right)-\left(\begin{array}{cc}-7& -3\\ -6& 1\end{array}\right)\end{array}$

Solution:
$\begin{array}{l}\left(a\right)\text{}\left(\begin{array}{l}9\\ 6\end{array}\right)-\left(\begin{array}{l}7\\ -2\end{array}\right)=\left(\begin{array}{l}9-7\\ 6-\left(-2\right)\end{array}\right)=\left(\begin{array}{l}2\\ 8\end{array}\right)\\ \\ \left(b\right)\text{}\left(\begin{array}{cc}3& -4\\ 0& 5\end{array}\right)-\left(\begin{array}{cc}-7& -3\\ -6& 1\end{array}\right)\\ =\left(\begin{array}{cc}3-\left(-7\right)& -4-\left(-3\right)\\ 0-\left(-6\right)& 5-1\end{array}\right)\\ =\left(\begin{array}{cc}3+7& -4+3\\ 0+6& 5-1\end{array}\right)=\left(\begin{array}{cc}10& -1\\ 6& 4\end{array}\right)\end{array}$

Example 3:

Given that $\left(\begin{array}{l}p\\ q\end{array}\right)+\left(\begin{array}{l}5p\\ 9\end{array}\right)=\left(\begin{array}{l}-12\\ 3q+1\end{array}\right)$  , find the values of p and q.

Solution:

$\begin{array}{l}\left(\begin{array}{l}p\\ q\end{array}\right)+\left(\begin{array}{l}5p\\ 9\end{array}\right)=\left(\begin{array}{l}-12\\ 3q+1\end{array}\right)\\ \left(\begin{array}{l}p+5p\\ q+9\end{array}\right)=\left(\begin{array}{l}-12\\ 3q+1\end{array}\right)\end{array}$

p + 5p = 12
6p = 12
p = 2
q + 9 = 3q + 1
q – 3q = 1 – 9
2q = 8
q = 4

Example 4:
Find the values of m and n in the following matrix equation.
$\left(\begin{array}{cc}7& 6\\ n& 1\end{array}\right)-\left(\begin{array}{cc}-1& m\\ -4& -2\end{array}\right)=\left(\begin{array}{cc}5& 12\\ 6& 11\end{array}\right)$

Solution:
$\left(\begin{array}{cc}7& 6\\ n& 1\end{array}\right)-\left(\begin{array}{cc}-1& m\\ -4& -2\end{array}\right)=\left(\begin{array}{cc}5& 12\\ 6& 11\end{array}\right)$

6 – m = 12
–m = 6
m = –6
n – (–4) = 6
n + 4 = 6
n = 2