Answer to Question #52683 in Linear Algebra for ravish

Question

a)Show that, if A is any n×n matrix with real entries, then there is a n×n symmetric matrix S and a n×n skew symmetric matrix S' such that A=S+S'.(3)b)Find the solutions to the following system of equations by reducing the corresponding augmented matrix to row-reduced echelon form.
2a+3b+4c+d=8
a+2b+2c+2d=3
a−b+c+3d=3