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  • If the matrix [0 a 3] is a skew symmetric matrix, find the values of a, b and c.

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

Answers (1)

A matrix is said to be skew-symmetric if A = -A’

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

As, A is skew symmetric matrix.

∴ A = -A’

\begin{array}{l} \left[\begin{array}{ccc} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{array}\right]=-\left[\begin{array}{ccc} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{array}\right]^{T} \\\\ \left[\begin{array}{ccc} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{array}\right]=-\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]=\left[\begin{array}{ccc} 0 & -2 & -c \\ -a & -b & -1 \\ -3 & 1 & 0 \end{array}\right]} \end{array}

Equating the respective elements of both matrices, as both the matrices are equal to each other we have,

a = -2 ; c = -3 ; b = -b ⇒ 2b = 0 ⇒ b = 0

Thus, we get,

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

 

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