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 $B$ is

• 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

Answer: (B)

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

$[A-2b=\left[\begin{array}{cc}1& -2\\ 3& 0\end{array}\right]](+2)$

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

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

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

Adding both equations

$-B=\left[\begin{array}{cc}2+3& -4-3\\ 6-1& 0+1\end{array}\right]$

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