Question

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

• A. $\lambda \ne -17$
• B. $\lambda \ne -18$
• C. $\lambda \ne -19$
• D. $\lambda \ne -20$

Answer 1

Answer: (A)

For invertible matrix, $\left|\begin{array}{ccc}\lambda & -1& 4\\ -3& 0& 1\\ -1& 1& 2\end{array}\right|\ne 0$
$\Rightarrow \lambda (0-1)+1(-6+1)+4(-3-0)\ne 0$
$\Rightarrow -\lambda -5-12\ne 0$
$\Rightarrow \lambda \ne -17$