Question

If $2A+B=\left[\begin{array}{cc}6& 4\\ 6& -11\end{array}\right]$ and $A-B=\left[\begin{array}{cc}0& 2\\ 6& 2\end{array}\right]$, then $A=$

• A. $\left[\begin{array}{cc}2& 2\\ 4& -3\end{array}\right]$
• B. $\left[\begin{array}{cc}2& 0\\ 4& -3\end{array}\right]$
• C. $\left[\begin{array}{cc}2& 2\\ 4& 3\end{array}\right]$
• D. None of these

Answer 1

The correct option is A $\left[\begin{array}{cc}2& 2\\ 4& -3\end{array}\right]$

$2A+B=\left[\begin{array}{cc}6& 4\\ 6& -11\end{array}\right]$ ....(1)
$A-B=\left[\begin{array}{cc}0& 2\\ 6& 2\end{array}\right]$ ....(2)

Adding (1) and (2): $2A+B+A-B=3A=\left[\begin{array}{cc}6+0& 4+2\\ 6+6& -11+2\end{array}\right]=\left[\begin{array}{cc}6& 6\\ 12& -9\end{array}\right]$
$A=\left[\begin{array}{cc}2& 2\\ 4& -3\end{array}\right]$
Ans: A