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Question
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
Options
True
False
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Solution
This statement is True.
Explanation:
Let A, B and C be three matrices of the same order.
Given that A' = A, B' = B and C' = C
Let P = A + B + C
⇒ P' = (A + B + C)'
= A' + B' + C'
= A + B + C
= P
So, A + B + C is also a symmetric matrix.
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