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Let X and Y be two arbitrary, 3 × 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 × 3, non zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?
  • a)
    Y3Z4 – Z4Y3
  • b)
    X44 + Y44
  • c)
    X4Z3 – Z3X4
  • d)
    X23 + Y23
Correct answer is option 'C,D'. Can you explain this answer?
Verified Answer
Let X and Y be two arbitrary, 3 × 3, non-zero, skew-symmetric ma...
X ' = –X, Y ' = –Y, Z ' = Z
(Y3Z4 – Z4Y3)' = (Z4)'(Y3)' – (Y3)'(Z4)'
= (Z')4(Y')3 – (Y')3(Z')4
= –Z4Y3 + Y3Z4 = Y3Z4 – Z4Y3
∴ Symmetric matrix.
Similarly X44 + Y44 is symmetric matrix and X4Z3 – Z3X4 and X23 + Y23 are skew symmetric matrices.
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Let X and Y be two arbitrary, 3 × 3, non-zero, skew-symmetric ma...
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Let X and Y be two arbitrary, 3 × 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 × 3, non zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?a)Y3Z4 – Z4Y3b)X44 + Y44c)X4Z3 – Z3X4d)X23 + Y23Correct answer is option 'C,D'. Can you explain this answer?
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