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CBSE Class 12 Math 2024 All Sets Solved Paper
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Question : 19 of 20
Marks:
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Assertion (A): For any symmetric matrix A, B’AB is a skew-symmetric matrix.
Reason (R): A square matrix P is skew-symmetric if P’ = – P.
Reason (R): A square matrix P is skew-symmetric if P’ = – P.
Solution:
If A is symmetric matrix then A' = A ........(1)
Now (B'AB)' = [B'(AB)]'
= (AB)'(B')' (by using formula (AB)' = B'A')
= B'A'B
= B'AB (by substituting (1))
Which gives B'AB is symmetric matrix. So Assertion (A) is false.
By definition a square matrix A is said to be skew-symmetric if A' = -A. So Reason (R) is true.
Now (B'AB)' = [B'(AB)]'
= (AB)'(B')' (by using formula (AB)' = B'A')
= B'A'B
= B'AB (by substituting (1))
Which gives B'AB is symmetric matrix. So Assertion (A) is false.
By definition a square matrix A is said to be skew-symmetric if A' = -A. So Reason (R) is true.
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