If matrix $\begin{bmatrix} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then find the values of $a, b$ and $c$.

$a = -2, b = 0, c = -3$

The correct answer is Option (1) → $a = -2, b = 0, c = -3$ ##

Let $A = \begin{bmatrix} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{bmatrix}$

Since, $A$ is skew-symmetric matrix.

$∴A' = -A$

$\Rightarrow \begin{bmatrix} 0 & 2 & c \\ a & b & 1 \\ 3 & -1 & 0 \end{bmatrix} = - \begin{bmatrix} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{bmatrix}$

$\Rightarrow \begin{bmatrix} 0 & 2 & c \\ a & b & 1 \\ 3 & -1 & 0 \end{bmatrix} = \begin{bmatrix} 0 & -a & -3 \\ -2 & -b & 1 \\ -c & -1 & 0 \end{bmatrix}$

Since, both matrices are equal.

$∴$ On comparing the corresponding elements of both sides, we get

$a = -2, c = -3 \text{ and } b = -b \Rightarrow b = 0$

$∴a = -2, b = 0 \text{ and } c = -3$