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. no real values of $\lambda ,\mu$ are possible
• D. none of these

Answer 1

The correct option is A $\lambda =3,\mu =-4$

Given,

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

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

Comparing both sides we get

$2\mu +9=1⟹2\mu =-8⟹\mu =-4$

Also $5+2\lambda =-1⟹2\lambda =6⟹\lambda =3$

Hence, we get $\mu =-4,\lambda =3.$