If \(A=\begin{bmatrix}2&1&-1\\0&1&2\\2&-1&\lambda\end{bmatrix}\) is a singular matrix, then the value of \(\lambda\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → -5
A singular matrix has determinant 0. Expanding along the first column (it contains a 0):
\( \displaystyle |A| = 2\begin{vmatrix}1&2\\-1&\lambda\end{vmatrix} - 0 + 2\begin{vmatrix}1&-1\\1&2\end{vmatrix} \)
\(= 2(\lambda + 2) + 2(2 + 1)\)
\(= 2\lambda + 10\)
Setting \(|A| = 0\):
\(2\lambda + 10 = 0,\quad \lambda = -5\)