If A = begin{bmatrix} -2 & 1 3 & 4 end{bmatr | vedclass

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(A) Any square matrix $A$ can be expressed as the sum of a symmetric matrix $P$ and a skew-symmetric matrix $Q$,where $P = \frac{1}{2}(A + A^T)$ and $

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$\begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix}$

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(A) Any square matrix $A$ can be expressed as the sum of a symmetric matrix $P$ and a skew-symmetric matrix $Q$,where $P = \frac{1}{2}(A + A^T)$ and $Q = \frac{1}{2}(A - A^T)$.Given $A = \begin{bmatrix} -2 & 1 \ 3 & 4 \end{bmatrix}$.Then $A^T = \begin{bmatrix} -2 & 3 \ 1 & 4 \end{bmatrix}$.Now,$A - A^T = \begin{bmatrix} -2 & 1 \ 3 & 4 \end{bmatrix} - \begin{bmatrix} -2 & 3 \ 1 & 4 \end{bmatrix} = \begin{bmatrix} 0 & -2 \ 2 & 0 \end{bmatrix}$.Therefore,$Q = \frac{1}{2}(A - A^T) = \frac{1}{2} \begin{bmatrix} 0 & -2 \ 2 & 0 \end{bmatrix} = \begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix}$.

Factory	Men and Women Workers
$I$	$30$ Men,$25$ Women
$II$	$25$ Men,$31$ Women
$III$	$27$ Men,$26$ Women

If $A = \begin{bmatrix} -2 & 1 \\ 3 & 4 \end{bmatrix}$ and $A = P + Q$,where $P$ is a symmetric matrix and $Q$ is a skew-symmetric matrix,then $Q$ is:

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