Question

If $2A+3B=$ $\left[\begin{array}{ccc}2& -1& 4\\ 3& 2& 5\end{array}\right]$ and $A+2B=$ $\left[\begin{array}{ccc}5& 0& 3\\ 1& 6& 2\end{array}\right],$ then $B$ is

• A. $\left[\begin{array}{ccc}8& -1& 2\\ -1& 10& -1\end{array}\right]$
• B. $\left[\begin{array}{ccc}8& 1& 2\\ -1& 10& -1\end{array}\right]$
• C. $\left[\begin{array}{ccc}8& 1& -2\\ -1& 10& -1\end{array}\right]$
• D. $\left[\begin{array}{ccc}8& 1& 2\\ 1& 10& 1\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{ccc}8& 1& 2\\ -1& 10& -1\end{array}\right]$

Since, $2A+3B=\left[\begin{array}{ccc}2& -1& 4\\ 3& 2& 5\end{array}\right]$ …………$\left(1\right)$

$A+2B=\left[\begin{array}{ccc}5& 0& 3\\ 1& 6& 2\end{array}\right]$ ………….$\left(2\right)$

$2\times$ Equation $\left(2\right)-$ Equation $\left(1\right)$

$\Rightarrow 2A+4B-2A-3B=\left[\begin{array}{ccc}10-2& 0+1& 6-4\\ 2-3& 12-2& 4-5\end{array}\right]$

$\Rightarrow B=\left[\begin{array}{ccc}8& 1& 2\\ -1& 10& -1\end{array}\right]$