Question

Let a matrix $A=\left[\begin{array}{cc}2& 3\sin x\\ 4\cos x& -1\end{array}\right],x\in R,$ then the maximum value of sum of minors of elements of $A$ is

Answer 1

Given : $A=\left[\begin{array}{cc}2& 3\sin x\\ 4\cos x& -1\end{array}\right]$
$\Rightarrow M_{11}=-1,M_{12}=4\cos x,M_{21}=3\sin x,M_{22}=2$
$\Rightarrow$Sum of minors $=1+3\sin x+4\cos x$
We know, $|3\sin x+4\cos x|\le \sqrt{3^2+4^2}$
So, maximum value of sum of minors $=6$