JEE-Advanced 2015 (9/40)
Let
and
be two arbitrary,
, non-zero, skew-symmetric matrices and
be an arbitrary,
, non-zero , symmetric matrix. Then which of the following matrices is (are) skew-symmetric ?
Note :
-
Submit your answer as the increasing order of the serial numbers of all the correct options.
-
For eg, if your answer is , then submit 12 as the correct answer, if your answer is , then submit 234 as the correct answer.
The answer is 34.
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1 solution
(C) ( X 4 Z 3 − Z 3 X 4 ) T = ( X 4 Z 3 ) T − ( Z 3 X 4 ) T = ( Z T ) 3 ( X T ) 4 − ( X T ) 4 ( Z T ) 3 = Z 3 X 4 − X 4 Z 3 = − ( X 4 Z 3 − Z 3 X 4 )
(D) ( X 2 3 + Y 2 3 ) T = ( X T ) 2 3 + ( Y T ) 2 3 = ( − X ) 2 3 + ( − Y ) 2 3 = − ( X 2 3 + Y 2 3 )