Q. The matrix$\begin{bmatrix} \lambda & 1 & 0 \\ 0 & 2 & 3 \\ 0 & 0 & \lambda \end{bmatrix}$ is non- singular
A) For all real values of $\lambda$
B) Only when $\lambda = \pm \frac{1}{\sqrt{2}}$
C) Only when $\lambda \neq 0$
D) Only when $\lambda = 0$
Explanation
(c)
Given matrix is non-singular, then
$\left| \begin{array}{r}
\lambda\ \ 1\ \ 0 \\
0\ \ 2\ \ 3 \\
0\ \ 0\ \ \lambda
\end{array} \right| \neq 0$
$\Rightarrow \lambda(2\lambda - 0) \neq 0$
$\Rightarrow \ \lambda \neq 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.