If \(A =\begin{bmatrix}3&2a\\1&5\end{bmatrix}\) and \(B =\begin{bmatrix}2&3\\b&5\end{bmatrix}\) both are singular matrices, then \(a + b\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{65}{6}\)
A singular matrix has determinant 0.
\(|A| = 3 \times 5 - 2a \times 1 = 15 - 2a = 0\)
\( \displaystyle a = \frac{15}{2} \)
\(|B| = 2 \times 5 - 3 \times b = 10 - 3b = 0\)
\( \displaystyle b = \frac{10}{3} \)
So
\( \displaystyle a + b = \frac{15}{2} + \frac{10}{3} = \frac{45 + 20}{6} = \frac{65}{6} \)