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Civil Engg. (GATE) 2011

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Multiple Choice

[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?

  1. Both [S] and [D] are symmetric.
  2. Both [S] and [D] are skew-symmetric.
  3. [S] is skew-symmetric and [D] is symmetric.
  4. [S] is symmetric and [D] is skew-symmetric.
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