Q. 545.0( 1 Vote )

# For what value of

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 AT = -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,

1st row of A = (0 1 -2)

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

3rd row of A = (x -3 0)

In the formation of matrix AT,

1st column of AT = 1st row of A = (0 1 -2)

2nd column of AT = 2nd row of A = (-1 0 3)

3rd column of AT = 3rd row of A = (x -3 0)

So, Substituting the matrices –A and AT, we get

-A = AT We know by the property of matrices, This implies,

a11 = b11, a12 = b12, a21 = b21 and a22 = b22

By comparing the corresponding elements of the two matrices,

x = 2

Thus, the value of x = 2.

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