If the matrix \(\begin{bmatrix}3&2a&-5\\4&0&b\\-5&3&10\end{bmatrix}\) is symmetric, then the value of \(5a + 2b\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16
In a symmetric matrix, \(a_{ij} = a_{ji}\) for every i and j.
Comparing the (1, 2) and (2, 1) entries:
\(2a = 4\)
\(a = 2\)
Comparing the (2, 3) and (3, 2) entries:
\(b = 3\)
The (1, 3) and (3, 1) entries are both −5, as needed. So
\(5a + 2b = 10 + 6 = 16\)