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