If \(\begin{bmatrix}-1 & 1 & 0\\a & b & 1\\1 & 2 & 1\end{bmatrix}\) is a singular matrix, then the relation between a and b is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(a + b = 3\)
A singular matrix has determinant 0. Expanding along the first row:
\( \displaystyle \begin{vmatrix}-1 & 1 & 0\\a & b & 1\\1 & 2 & 1\end{vmatrix} = -1\begin{vmatrix}b & 1\\2 & 1\end{vmatrix} - 1\begin{vmatrix}a & 1\\1 & 1\end{vmatrix} + 0 \)
\(= -(b - 2) - (a - 1)\)
\(= 3 - (a + b)\)
Setting it equal to 0:
\(a + b = 3\)