Civil Engg. (GATE) 2011

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Question 1 of 65

[A] is a square matrix which is neither symmetric nor skew-symmetric and [A]^T is its transpose. The sum and difference of these matrices are defined as [S] = [A] + [A]^T and [D] = [A] – [A]^T respectively. Which of the following statements is TRUE?

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Both [S] and [D] are symmetric.

Both [S] and [D] are skew-symmetric.

[S] is skew-symmetric and [D] is symmetric.

[S] is symmetric and [D] is skew-symmetric.

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