Question

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

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

Answer 1

The correct option is B $\left[\begin{array}{cc}-5& 7\\ -5& -1\end{array}\right]$

Given , $A-2B=\left[\begin{array}{cc}1& -2\\ 3& 0\end{array}\right]$

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

Also given, $2A-3B=\left[\begin{array}{cc}-3& 3\\ 1& -1\end{array}\right]$ ....(ii)

Subtracting (i) from (ii), we get

$B=\left[\begin{array}{cc}-5& 7\\ -5& -1\end{array}\right]$