Question

$\text{If}3A-B=\left[\begin{array}{cc}5& 0\\ 1& 1\end{array}\right]\text{and}B=\left[\begin{array}{cc}4& 3\\ 2& 5\end{array}\right],$
then find the matrix $A.$

Answer 1

Let us take the given matrix equations
$3A-B=\left[\begin{array}{cc}5& 0\\ 1& 1\end{array}\right]\cdots \left(1\right)B=\left[\begin{array}{cc}4& 3\\ 2& 5\end{array}\right]\cdots \left(2\right)$

To find matrix $A$,
Let us take $\text{eq}\left(1\right)+\text{eq}\left(2\right)$, we get

$3A=\left[\begin{array}{cc}9& 3\\ 3& 6\end{array}\right]\therefore A=\frac{1}{3}\left[\begin{array}{cc}9& 3\\ 3& 6\end{array}\right]=\left[\begin{array}{cc}3& 1\\ 1& 2\end{array}\right]$