Question

If $A=\left[\begin{array}{cc}1& 2\\ -3& 1\end{array}\right]\text{and}B=\left[\begin{array}{cc}11& -1\\ 4& 3\end{array}\right]$

Find Matrix X, given that
X-5A=3B

• A. $\left[\begin{array}{cc}8& 7\\ 3& 14\end{array}\right]$
• B. $\left[\begin{array}{cc}8& 7\\ -3& -4\end{array}\right]$
• C. $\left[\begin{array}{cc}38& -7\\ 3& 14\end{array}\right]$
• D. $\left[\begin{array}{cc}38& 7\\ -3& 14\end{array}\right]$

Answer 1

The correct option is D

$\left[\begin{array}{cc}38& 7\\ -3& 14\end{array}\right]$

Given $X-5A=3B\Rightarrow X=3B+5A$

$A=\left[\begin{array}{cc}1& 2\\ -3& 1\end{array}\right]\text{and}B=\left[\begin{array}{cc}11& -1\\ 4& 3\end{array}\right]$

$5A=\left[\begin{array}{cc}5\times 1& 5\times 2\\ 5\times (-3)& 5\times 1\end{array}\right]=\left[\begin{array}{cc}5& 10\\ -15& 5\end{array}\right]$

$3B=\left[\begin{array}{cc}3\times 11& 3\times (-1)\\ 3\times 4& 3\times 3\end{array}\right]=\left[\begin{array}{cc}33& -3\\ 12& 9\end{array}\right]$

$3B+5A=\left[\begin{array}{cc}38& 7\\ -3& 14\end{array}\right]$