Question

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

• A. $\left[\begin{array}{cc}-4& -5\\ -6& -7\end{array}\right]$
• B. $\left[\begin{array}{cc}0& 6\\ -3& 7\end{array}\right]$
• C. $\left[\begin{array}{cc}2& -1\\ 3& 2\end{array}\right]$
• D. $\left[\begin{array}{cc}6& -1\\ 0& 1\end{array}\right]$

Answer 1

Answer: (A)

$\left[\begin{array}{cc}-4& -5\\ -6& -7\end{array}\right]$

Given, $A-2B=\left[\begin{array}{cc}1& 5\\ 3& 7\end{array}\right]$ and $2A-3B=\left[\begin{array}{cc}-2& 5\\ 0& 7\end{array}\right]$
$2A-4B=\left[\begin{array}{cc}2& 10\\ 6& 14\end{array}\right]$ -----(1)
$2A-3B=\left[\begin{array}{cc}-2& 5\\ 0& 7\end{array}\right]$ -------(2)
Subtracting $\left(1\right)$ from $\left(2\right)$ gives
$B=\left[\begin{array}{cc}-4& -5\\ -6& -7\end{array}\right]$
Hence, option $A.$