# Linear algebra systems ,Ax=b,Ax=0

## Homework Statement

Let be Ax=b any consistent system of linear equations, and let be x1 a fixed solution. Show that every solution to the system
can be written in the form x=x1 +x0, where x0 is a solution Ax=0 . Show also that every matrix of this form is a solution

## The Attempt at a Solution

well A(x1+x0)= Ax1+Ax0=b+0=b
but this only proves that any matrix x=x1+x0 is a solution but not that every solution can be written as such and i dont know how to prove that

HallsofIvy