Homogenous Equals Zero Solution Theorem

Given a Augmented Matrix system of equations in the form$[A|b]$, where $b$ is the constants and $A$ are the vectors,

• If $v_p$ is a soln to this matrix $[A|b]$
• If $v_h$ is a soln to $[A|0]$
• Then, $v_p+v_h$ is also a soln to this matrix $[A|b]$