The matrix [ ccc & -1 & 4 -3 & 0 & 1 -1 & 1 & 2 ] is invertible, … - Vidyadip

MCQ

The matrix $\left[\begin{array}{ccc}\lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{array}\right]$ is invertible, if

A
$\lambda \neq-15$
✓
$\lambda \neq-17$
C
$\lambda \neq-16$
D
$\lambda \neq-18$

✓

Answer

Correct option: B.

$\lambda \neq-17$

(B) The given matrix will be invertible, if
$\left|\begin{array}{ccc}\lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{array}\right| \neq 0$
$\begin{array}{l}\Rightarrow \lambda(0-1)+1(-6+1)+4(-3) \neq 0 \\ \Rightarrow-\lambda-5-12 \neq 0 \\ \Rightarrow \lambda \neq-17\end{array}$

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