Determinants Matrices Question 126
Question: If C is skew-symmetric matrix of order n and X is $ n\times 1 $ column matrix, then X’CX is a
Options:
A) Scalar matrix
B) Unit matrix
C) Null matrix
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Here, X is $ n\times 1, $ C is $ n\times n $ and $ X’ $ is $ 1\times n $ Hence, $ X’CX $ is $ 1\times 1 $ matrix. Let $ X’CX=k $ . Thus, $ (X’CX)’=X’C’X’=X’C’X’=X’(-C)X $
$ =-X’CX=-k $
$ \Rightarrow k=-k\Rightarrow k=0\Rightarrow X’CX $ is null matrix.
BETA
