$($Please do this without using Rank$)$ Let $A*x=b$ be a consistent linear system, where $Ain{M}_{mn},xin{M}_{n1}$ and $bin{M}_{m1}.$

Show that every solution $x$ of this system is written as $x=x_h+x_p,$ where $x_h$ is the

solution of the corresponding homogenous system $A*x=0$ and $x_p$ a particular solution of

$A*x=b.$pl