# Express the matrix A = [(3,-4)(1,-1)]  as the sum of a symmetric matrix and a skew-symmetric matrix.

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Express the matrix A = $\begin{bmatrix} 3 & -4 \\[0.3em] 1& -1 \\[0.3em] \end{bmatrix}$ as the sum of a symmetric matrix and a skew-symmetric matrix.

A = [(3,-4)(1,-1)]

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Given A = $\begin{bmatrix} 3 &-4 \\[0.3em] 1& -1 \\[0.3em] \end{bmatrix}$, to express as the sum of symmetric matrix P and skew symmetric matrix Q.

A = P + Q

Where P = $\frac{1}{2}$(A + A') and Q = $\frac{1}{2}$(A - A'), we will find transpose of matrix A

A' = $\begin{bmatrix} 3 &1 \\[0.3em] -4& -1 \\[0.3em] \end{bmatrix}$

Now using the above formulas

Hence A = P + Q

$\Rightarrow$ $\begin{bmatrix} 3 &-4 \\[0.3em] 1& -1 \\[0.3em] \end{bmatrix}$