The value of \(\lambda\) for which the matrix \(\begin{pmatrix} 1 & 0 & \lambda \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix}\) is a singular matrix is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1
A matrix is singular when its determinant is zero. Expanding along the first row:
\(1(1 \times 1 - 0 \times 0) - 0 + \lambda(0 \times 0 - 1 \times 1) = 0\)
\(1 - \lambda = 0\)
\(\lambda = 1\)