DETERMINANTS — Maths STD 12 Science — Question

4. $\text{None of these}$

Solution:

$\text{A}=\begin{bmatrix}2&\lambda&-3\\0&2&5\\1&1&3\end{bmatrix}$

The inverse of a matrix exists if its determinant is not equal to 0.

Consider,

$|\text{A}|=\begin{bmatrix}2&\lambda&-3\\0&2&5\\1&1&3\end{bmatrix}\neq0$

$\Rightarrow|\text{A}| = 2 (6 – 5) – \lambda (0 – 5) + (-3) (0 – 2)\neq0$

$\Rightarrow2 + 5\lambda + 6 \neq 0$

$\Rightarrow5\lambda + 8 \neq 0$

$\Rightarrow5\lambda \neq -8$

$\Rightarrow\lambda\neq\frac{-8}{5}$