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

16

The correct answer is Option (3) → 16

Given symmetric matrix:

$\begin{bmatrix} 3 & 2a & -5 \\ 4 & 0 & b \\ -5 & 3 & 10 \end{bmatrix}$

For symmetry: $a_{ij} = a_{ji}$.

Compare:

$(1,2)$ and $(2,1)$:

$2a = 4 \Rightarrow a = 2$

$(2,3)$ and $(3,2)$:

$b = 3$

Now compute:

$5a + 2b = 5(2) + 2(3) = 10 + 6 = 16$

The value of $5a + 2b$ is 16.