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

Question

Express the matrix \(\begin{bmatrix} 3 & -2 & -4 \\[0.3em] 3 & -2 & -5 \\[0.3em] -1 & 1& 2 \end{bmatrix}\) as the sum of a symmetric and skew-symmetric matrix and verify your result.

Answer 1

Given,

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

Then,

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

Let,

X + Y = A