Symmetric and Skew-Symmetric Matrix Quiz
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Questions and Answers

Which of the following statements is true about a symmetric matrix?

  • The determinant of a symmetric matrix is always negative.
  • The main diagonal entries are all equal to zero.
  • All entries above the main diagonal are negations of the corresponding entries below the main diagonal.
  • All entries above the main diagonal are equal to the corresponding entries below the main diagonal. (correct)

    • What is the relationship between a skew-symmetric matrix and its transpose?

  • They are reciprocals of each other.
  • They are negations of each other. (correct)
  • They are equal.
  • They are not related.

    • What is the rank of a skew-symmetric matrix?

  • It is always odd.
  • It is always even.
  • It is always zero. (correct)
  • It can be any non-negative integer.

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