If the matrix is a skew symmetric matrix, find the values of a, b and c.
$\left[\begin{array}{ccc}0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0\end{array}\right]$
Let $A=\left[\begin{array}{ccc}0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0\end{array}\right]$
As, $A$ is skew - symmetric matrix.
So, we have
$A^{\prime}=-A$
Then,
$\Rightarrow \quad\left[\begin{array}{ccc}0 & 2 & c \\ a & b & 1 \\ 3 & -1 & 0\end{array}\right]=-\left[\begin{array}{ccc}0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0\end{array}\right]$
$\Rightarrow \quad\left[\begin{array}{ccc}0 & 2 & c \\ a & b & 1 \\ 3 & -1 & 0\end{array}\right]=\left[\begin{array}{ccc}0 & -a & -3 \\ -2 & -b & 1 \\ -c & -1 & 0\end{array}\right]$
By equality of matrices, we get
$a=-2, c=-3$ and $b=-b \Rightarrow b=0$
Hence,
$a=-2, b=0$ and $c=-3$
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