Express the matrix A = [(3,-4)(1,-1)] as the sum of a symmetric and a skew-symmetric matrix. ​

Question

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

Answer 1

Given,

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

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

Let,

Hence, 

X is a symmetric matrix. 

Now let,