If C is a skew-symmetric matrix of order n and X is n x 1 column matrix, then…

2017

If C is a skew-symmetric matrix of order n and X is n x 1 column matrix, then XTCX is a

  1. A.

    scalar matrix

  2. B.

    null matrix

  3. C.

    unit matrix

  4. D.

    matrix will all elements 1

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Correct answer: B

Since C is skew-symmetric, its transpose satisfies the condition C^T = -C. The expression X^T CX results in a scalar value (1x1 matrix). Taking the transpose of the entire expression yields -(X^T CX), which implies the value equals its own negative. Consequently, the only possible solution is zero.

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