Question

If $\left[\begin{array}{cc}2& -3\\ 1& \lambda \end{array}\right]\times \left[\begin{array}{ccc}1& 5& \mu \\ 0& 2& -3\end{array}\right]=\left[\begin{array}{ccc}2& 4& 1\\ 1& -1& 13\end{array}\right]$ then

• A. $\lambda =3,\mu =4$
• B. $\lambda =4,\mu =3$
• C. $\lambda =2,\mu =5$
• D. none of these

Answer 1

The correct option is D. None of these

Since, $\left[\begin{array}{cc}2& -3\\ 1& \lambda \end{array}\right]\times \left[\begin{array}{ccc}1& 5& \mu \\ 0& 2& -3\end{array}\right]=\left[\begin{array}{ccc}2& 4& 1\\ 1& -1& 13\end{array}\right]$

$\Rightarrow \left[\begin{array}{ccc}2-0& 10-6& 2\mu +9\\ 1+0& 5+2\lambda & \mu -3\lambda \end{array}\right]=\left[\begin{array}{ccc}2& 4& 1\\ 1& -1& 13\end{array}\right]$

$\Rightarrow \left[\begin{array}{ccc}2& 4& 2\mu +9\\ 1& 5+2\lambda & \mu -3\lambda \end{array}\right]=\left[\begin{array}{ccc}2& 4& 1\\ 1& -1& 13\end{array}\right]$

$\Rightarrow 2\mu +9=1$ and $5+2\lambda =-1$
$\Rightarrow \mu =-4,\lambda =-3$
And these value satisfy $\mu -3\lambda =13$