# Matrices Short Questions (Question 1 - 4)

Question 1:
$\left(\begin{array}{cc}1& 4\\ 6& 2\end{array}\right)+3\left(\begin{array}{cc}2& 0\\ 4& -3\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)$
Solution:
$\begin{array}{l}\left(\begin{array}{cc}1& 4\\ 6& 2\end{array}\right)+3\left(\begin{array}{cc}2& 0\\ 4& -3\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)\\ =\left(\begin{array}{cc}1& 4\\ 6& 2\end{array}\right)+\left(\begin{array}{cc}6& 0\\ 12& -9\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)\\ =\left(\begin{array}{cc}7& 4\\ 18& -7\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)\\ =\left(\begin{array}{cc}7-\left(-3\right)& 4-0\\ 18-\left(-2\right)& -7-\left(-5\right)\end{array}\right)\\ =\left(\begin{array}{cc}10& 4\\ 20& -2\end{array}\right)\end{array}$

Question 2:
Find the value of m in the following matrix equation:
$\left(\begin{array}{cc}9& -4\\ 5& 0\end{array}\right)+\frac{1}{2}\left(\begin{array}{cc}8& m\\ 6& -10\end{array}\right)=\left(\begin{array}{cc}13& -7\\ -2& 1\end{array}\right)$
Solution:
$\begin{array}{l}\left(\begin{array}{cc}9& -4\\ 5& 0\end{array}\right)+\frac{1}{2}\left(\begin{array}{cc}8& m\\ 6& -10\end{array}\right)=\left(\begin{array}{cc}13& -7\\ -2& 1\end{array}\right)\\ -4+\frac{1}{2}m=-7\\ \frac{1}{2}m=-3\\ m=-6\end{array}$

Question 3:

Solution:
$\begin{array}{l}2x+8=-2\\ 2x=-10\\ x=-5\\ \\ 3y-12=6\\ 3y=18\\ y=6\end{array}$

Question 4:

Solution: