Question

Find the matrix $X$ if $X+\left[\begin{array}{cc}4& 6\\ -3& 7\end{array}\right]=\left[\begin{array}{cc}3& -6\\ 5& -8\end{array}\right]$

Answer 1

$\begin{array}{c}LetA=\left[\begin{array}{cc}4& 6\\ -3& 7\end{array}\right]andB=\left[\begin{array}{cc}3& -6\\ 5& -8\end{array}\right]\\ ThenthegivenmatrixequationisX+A=B.\\ \therefore X+A=B\Rightarrow X=B+\left(-A\right)\\ =\left[\begin{array}{cc}3& -6\\ 5& -8\end{array}\right]+\left[\begin{array}{cc}-4& -6\\ 3& -7\end{array}\right]\\ =\left[\begin{array}{cc}3+\left(-4\right)& -6+\left(-6\right)\\ 5+3& -8+\left(-7\right)\end{array}\right]\\ =\left[\begin{array}{cc}-1& -12\\ 8& -15\end{array}\right]\\ Hence,\\ X=\left[\begin{array}{cc}-1& -12\\ 8& -15\end{array}\right]\end{array}$

Hence, this is the answer.