Easy# Classifying Solutions

LINALG-HVJ3ZE

Suppose that you are given a linear system $A \mathbf{x} = \mathbf{b}$ with augmented matrix $M = [ A | \mathbf{b}]$. Suppose that $A$ has $4$ columns.

If the rank of $A$ and the rank of $M$ are both $3$, then classify the solutions of the system.