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Write A = 4, -2, 5; 0, 3, 1; 7, -3, 2 as S + K, where S is symmetric and K is skew-symmetric…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Write $A =

\displaystyle \begin{bmatrix} 4 & -2 & 5 \\ 0 & 3 & 1 \\ 7 & -3 & 2 \end{bmatrix}

$as$ S + K $, where$ S $is symmetric and$ K $is skew-symmetric. Give the entries of$ S $in row$ 1 $, column$ 3 $and in row$ 1 $, column$ 2 $, and the entry of$ K $in row$ 2 $, column$ 3$.

Need a reminder? The key ideaShow

$(AB)^T = B^TA^T$ . A matrix is symmetric if $A^T = A$ and skew-symmetric if $A^T = -A$ . Every square matrix is $\tfrac{1}{2}(A + A^T) + \tfrac{1}{2}(A - A^T)$ , a symmetric part plus a skew-symmetric part.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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