Express the following matrix as the sum of a symmetric and skew symmetric matrix, and verify your result.[(3,-2,-4)(3,-2,-5)(-1,1,2)]

Question

Express the following matrix as the sum of a symmetric and skew symmetric matrix, and verify your result.

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

Answer 1

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

A can be expressed as,

Where, A + A' and A - A'are symmetric and skew symmertic matrices  respectively.

Now,

Putting these values in (i) we get

Verification :