Expressing as a sum of symmetric and skew symmetric matrix
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Express the following matrices as the of a symmetric and a skew symmetric matrix:(i) displaystyle begin{bmatrix} 3 & 5 1 & -1 end{bmatrix}(ii) displaystyle left[ begin{matrix} 6 -2 2 end{matrix}begin{matrix} -2 3 -1 end{matrix}begin{matrix} 2 -1 3 end{matrix} right] (iii) displaystyle left[ begin{matrix} 3 -2 -4 end{matrix}begin{matrix} 3 -2 -5 end{matrix}begin{matrix} -1 1 2 end{matrix} right] (iv) displaystyle begin{bmatrix} 1 & 5 -1 & 2 end{bmatrix}
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