Question

If $2A+B^T=\left[\begin{array}{cc}2& -3\\ 4& 7\end{array}\right]$ and $A^T-B=\left[\begin{array}{cc}4& -5\\ 0& 1\end{array}\right]$, then $A$ is equal to

• A. $\frac{1}{3}\left[\begin{array}{cc}6& -3\\ -1& 8\end{array}\right]$
• B. $\left[\begin{array}{cc}2& -3\\ -1& 8\end{array}\right]$
• C. $\frac{1}{2}\left[\begin{array}{cc}2& 3\\ -1& 8\end{array}\right]$
• D. $\left[\begin{array}{cc}3& -3\\ -1& 8\end{array}\right]$

Answer 1

The correct option is A $\frac{1}{3}\left[\begin{array}{cc}6& -3\\ -1& 8\end{array}\right]$

$2A+B^T=\left[\begin{array}{cc}2& -3\\ 4& 7\end{array}\right]\cdots \left(i\right)$ and
$A-B^T=\left[\begin{array}{cc}4& 0\\ -5& 1\end{array}\right]\cdots \left(ii\right)$
Adding $\left(i\right)$ and $\left(ii\right)$
$\Rightarrow 3A=\left[\begin{array}{cc}6& -3\\ -1& 8\end{array}\right]$