Question

If matrix $A=\left[\begin{array}{cc}2& y\\ 2y& 8\end{array}\right]$ is non-singular, then the value(s) of $y$ can be

• A. $-\sqrt{2}$
• B. $-2\sqrt{2}$
• C. $\sqrt{2}$
• D. $4\sqrt{2}$

Answer 1

Answer: (A), (C), (D)

$4\sqrt{2}$

Given : $A=\left[\begin{array}{cc}2& y\\ 2y& 8\end{array}\right]$
For non-singular matrix :$|A|\ne 0$
$\Rightarrow 16-2y^2\ne 0$
$\Rightarrow y\ne \pm 2\sqrt{2}$