If $A=\begin{bmatrix}2&1&-1\\0&1&2\\2&-1&λ\end{bmatrix}$ is a singular matrix, then the value of $λ$ is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → -5
$A=\begin{pmatrix}2&1&-1\\0&1&2\\2&-1&\lambda\end{pmatrix}$
$\det(A)=2\begin{vmatrix}1&2\\-1&\lambda\end{vmatrix} -1\begin{vmatrix}0&2\\2&\lambda\end{vmatrix} -1\begin{vmatrix}0&1\\2&-1\end{vmatrix}$
$=2(\lambda+2)\;-\;(-4)\;-\;(-2)$
$=2(\lambda+2)\;+\;4\;+\;2$
$=2\lambda+10$
For a singular matrix: $2\lambda+10=0$
$\lambda=-5$
The required value of $\lambda$ is $-5$.