Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix: (i) [(4,2),(3,-5)] and

Question

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

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

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

Answer 1

(i) Let 

(ii) Let 

Now,