Answer :

We are given that,

is a skew-symmetric matrix.

We need to find the value of x.

Let us understand what skew-symmetric matrix is.

A skew-symmetric matrix is a square matrix whose transpose equals its negative, that, it satisfies the condition

A skew symmetric matrix ⬄ A^{T} = -A

First, let us find –A.

Let us find the transpose of A.

We know that the transpose of a matrix is a new matrix whose rows are the columns of the original.

In matrix A,

1^{st} row of A = (0 1 -2)

2^{nd} row of A = (-1 0 3)

3^{rd} row of A = (x -3 0)

In the formation of matrix A^{T},

1^{st} column of A^{T} = 1^{st} row of A = (0 1 -2)

2^{nd} column of A^{T} = 2^{nd} row of A = (-1 0 3)

3^{rd} column of A^{T} = 3^{rd} row of A = (x -3 0)

So,

Substituting the matrices –A and A^{T}, we get

-A = A^{T}

We know by the property of matrices,

This implies,

a_{11} = b_{11}, a_{12} = b_{12}, a_{21} = b_{21} and a_{22} = b_{22}

By comparing the corresponding elements of the two matrices,

x = 2

Thus, the value of x = 2.

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