Question

maths question plz help me to solve​

Answer 1

Answer:

$\frac{1}{2} \left[\begin{array}{cc}8&1\\1&-10\end{array}\right] + \frac{1}{2} \left[\begin{array}{cc}0&-5\\5&0\end{array}\right]$

explanation:

Sum of symmetric and skew symmetric matrix = 1/2(A + A') + 1/2(A + A')

A = $\left[\begin{array}{cc}4&-2&\\3&-5&\end{array}\right]$    , A'     = $\left[\begin{array}{cc}4&3\\-2&-5\end{array}\right]$

(A + A')  = $\left[\begin{array}{cc}4&-2&\\3&-5&\end{array}\right] + \left[\begin{array}{cc}4&3\\-2&-5\end{array}\right]$    

= $\left[\begin{array}{cc}8&1\\1&-10\end{array}\right]$

(A - A') = $\left[\begin{array}{cc}4&-2&\\3&-5&\end{array}\right] - \left[\begin{array}{cc}4&3\\-2&-5\end{array}\right]$

          =$\left[\begin{array}{cc}0&-5\\5&0\end{array}\right]$

Now,  1/2(A + A') + 1/2(A - A')

$\frac{1}{2} \left[\begin{array}{cc}8&1\\1&-10\end{array}\right] + \frac{1}{2} \left[\begin{array}{cc}0&-5\\5&0\end{array}\right]$