Question

`If A = ([3   5] , [7     9])` is written as A = P + Q, where as A = p + Q , Where  P is a symmetric matrix and Q is skew symmetric matrix , then wqrite the matrix P. 

Answer 1

\[A = \begin{bmatrix}3 & 5 \\ 7 & 9\end{bmatrix}\]

P is symmetric matrix. So, 

\[P = \frac{1}{2}\left( A + A^T \right)\] 

Q is skew symmetric matrix. So, 

\[Q = \frac{1}{2}\left( A - A^T \right)\]

\[A^T = \begin{bmatrix}3 & 7 \\ 5 & 9\end{bmatrix}\] 

\[P = \frac{1}{2}\begin{bmatrix}6 & 12 \\ 12 & 18\end{bmatrix} = \begin{bmatrix}3 & 6 \\ 6 & 9\end{bmatrix}\]