The matrix \(\begin{bmatrix}x - 1 & 3 & 5\\ 0 & x + 2 & 7\\ 0 & 0 & 2\end{bmatrix}\) is singular if
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(x = 1\) or \(x = -2\)
All entries below the diagonal are zero, so the determinant is the product of the diagonal entries:
\(|A| = 2(x - 1)(x + 2)\)
The matrix is singular when \(|A| = 0\):
\((x - 1)(x + 2) = 0\)
So \(x = 1\) or \(x = -2\), and each of these makes one diagonal entry zero.