If the matrix $\begin{bmatrix}0&7&-12\\-7&0&-5\\2a&5&3b\end{bmatrix}$ is skew-symmetric, then the value of $(4a+3b)$ is:

24

The correct answer is Option (1) → 24

Given matrix

$A=\begin{pmatrix}0&7&-12\\-7&0&-5\\2a&5&3b\end{pmatrix}$

For skew-symmetric matrix

$A^T=-A$

Hence $a_{ij}=-a_{ji}$

From positions $(1,3)$ and $(3,1)$

$-12=-2a$

$2a=12$

$a=6$

From diagonal element $(3,3)$

$3b=0$

$b=0$

Now compute $4a+3b$

$=4(6)+3(0)$

$=24$

The value of $4a+3b$ is $24$.