ISRO | ISRO CS 2017 | Question 17
If C is a skew-symmetric matrix of order n and X is n x 1 column matrix, then XTCX is a
(A) scalar matrix
(B) null matrix
(C) unit matrix
(D) matrix will all elements 1
Answer: (B)
Explanation: A is skew symmetric of order n X n,order of X = n x 1 and order of X’ = 1 x n, then order of
X'AX = ((1 X n)(n X n))(n X 1)
= (1 X n)(n X 1) = 1
Let X'AX = Y
(X'AX)' = Y'
X'A'X" = Y' (since (AB)' = B'A')
As A is a skew-symmetric matrix, A' = -A
X'(-A)X" = Y'
-(X'AX) = Y
-Y = Y
Y = 0
So, option (B) is correct.
Quiz of this Question
Last Updated :
16 Mar, 2018
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...