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COMEDK20269 May 2026Evening ShiftMathematicsMatricesActual

If the matrix M = bmatrix x+5 & a & -4 -2 & 0 & b c & 6 & y+1 bmatrix is a skew symmetric matrix, the value of the expression ab + c^2 - xy is:

Options

  1. A0
  2. B-9
  3. C-1
  4. D-33

Correct answer

C. -1

Step-by-step solution

For a skew-symmetric matrix M , M^T = -M . The diagonal elements must be zero: x + 5 = 0 x = -5 y + 1 = 0 y = -1 For non-diagonal elements, m_ ij = -m_ ji : m₁₂ = -m₂₁ a = -(-2) = 2 m₁₃ = -m₃₁ -4 = -c c = 4 m₂₃ = -m₃₂ b = -6 Substituting these values into the expression ab + c^2 - xy : ab + c^2 - xy = (2)(-6) + (4)^2 - (-5)(-1) = -12 + 16 - 5 = -1 Answer: -1

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