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Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(i) \(\begin{bmatrix} 3&5 \\[0.3em] 1& -1 \\[0.3em] \end{bmatrix}\)

(ii) \(\begin{bmatrix} 6&-2& 2\\[0.3em] -2 &3 &-1\\[0.3em] 2 & -1& 3 \end{bmatrix}\)

(iii) \(\begin{bmatrix} 3&3& -1 \\[0.3em] -2& -2 &1 \\[0.3em] -4 &-5 &2 \end{bmatrix}\)

(iv) \( = \begin{bmatrix} 1 &5 \\[0.3em] -1& 2 \\[0.3em] \end{bmatrix}\)

1 Answer

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∴ B is symmetrix matrix.

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