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COMEDK · Maths · 21. Matrices

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

  1. A \(0\)
  2. B \(-9\)
  3. C \(-1\)
  4. D \(-33\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-1\)

Step-by-step Solution

Detailed explanation

For a skew-symmetric matrix \(M\), \(M^T = -M\). The diagonal elements must be zero: \(x + 5 = 0 \Rightarrow x = -5\) \(y + 1 = 0 \Rightarrow y = -1\) For non-diagonal elements, \(m_{ij} = -m_{ji}\): \(m_{12} = -m_{21} \Rightarrow a = -(-2) = 2\)…