Question

Consider the matrix $A=\left[\begin{array}{cc}3& 2\sin x\\ 1& -2\end{array}\right],$ where $x\in R.$ Then the maximum value of sum of minors of all elements of $A$ is

[2 marks]

• A. $0$
• B. $6$
• C. $4$
• D. $3$

Answer 1

The correct option is C $4$

$A=\left[\begin{array}{cc}3& 2\sin x\\ 1& -2\end{array}\right]$
$\Rightarrow M_{11}=-2,M_{12}=1$
$M_{21}=2\sin x,M_{22}=3$
Now, sum of minors $=2+2\sin x$
Since $-1\le \sin x\le 1,$
so maximum value of sum of minors $=4$