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AP EAMCET · Maths · Matrices

If \(A=\left[\begin{array}{cc}-2 & 1 \\ 3 & 4\end{array}\right]\) and \(\mathrm{A}=\mathrm{P}+\mathrm{Q}\), where \(\mathrm{P}\) is symmetric matrix and \(\mathrm{Q}\) is Skew-Symmetric matrix; then Q is

  1. A \(\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]\)
  2. B \(\left[\begin{array}{cc}0 & 2 \\ -2 & 0\end{array}\right]\)
  3. C \(\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\)
  4. D \(\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\)

Step-by-step Solution

Detailed explanation

\(A^T = \left[\begin{array}{cc}-2 & 3 \\ 1 & 4\end{array}\right]\) \(Q = \frac{1}{2}(A - A^T) = \frac{1}{2}\left(\left[\begin{array}{cc}-2 & 1 \\ 3 & 4\end{array}\right] - \left[\begin{array}{cc}-2 & 3 \\ 1 & 4\end{array}\right]\right)\)…