Chapter 9.3, Problem 15E

Prove that if ${\text{x}}_p$ satisfy ${\text{Ax}}_p=\text{b}$, then every solution of the nonhomogeneous system $\text{Ax}=\text{b}$ is of the form $\text{x}={\text{x}}_p+{\text{x}}_h$, where ${\text{x}}_h$ is a solution to the corresponding homogeneous system $\text{Ax}=0$.