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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