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AP EAMCET · Maths · Matrices

If \(A=\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]\) is expressed as a sun of a symmetric matrix \(\mathrm{P}\) and skew symmetric matrix \(\mathrm{Q}\), then \(\mathrm{P}^{\mathrm{T}}-\mathrm{Q}^{\mathrm{T}}=\)

  1. A \(\left[\begin{array}{ccc}8 & -16 & -4 \\ 2 & 8 & 7 \\ 6 & 14 & -16\end{array}\right]\)
  2. B \(\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]\)
  3. C \(\left[\begin{array}{ccc}2 & 4 & -5 \\ 0 & 3 & 7 \\ -3 & 1 & 2\end{array}\right]\)
  4. D \(\left[\begin{array}{ccc}1 & 0 & -3 / 2 \\ 2 & 3 / 2 & 1 / 2 \\ -5 / 2 & 7 / 2 & 1\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]\)

Step-by-step Solution

Detailed explanation

Given : \(A=\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]\) Since, each and every matrix can be written as sum of symmetric \& skew symmetric matrix. \(\therefore\) A can be written as sum symmetric matrix \(P\) and skew symmetric matrix Q.…