Question

If $A=\left[\begin{array}{cc}6& 2\\ 5& -4\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 2\\ -5& 1\end{array}\right]$, find a matrix $X$ such that $2A+3B-5X=0$

Answer 1

According to question,

$2A+3B-5X=0$

$\Rightarrow$ $5X=2A+3B$

$\Rightarrow$ $5X=2\left[\begin{array}{cc}6& 2\\ 5& -4\end{array}\right]+3\left[\begin{array}{cc}1& 2\\ -5& 1\end{array}\right]$

$\Rightarrow$ $5X=\left[\begin{array}{cc}12& 4\\ 10& -8\end{array}\right]+\left[\begin{array}{cc}3& 6\\ -15& 3\end{array}\right]$

$\Rightarrow$ $X=\frac{1}{5}\left[\begin{array}{cc}15& 10\\ -5& -5\end{array}\right]$

$\Rightarrow$ $X=\left[\begin{array}{cc}3& 2\\ -1& -1\end{array}\right]$