> [!NOTE] Lemma > Let $A$ be a [[Real Matrices|real matrix]] of order $m\times n.$ If $EA$ is the [[Reduced Row Echelon Form for Real Matrix|RREF]] of $A,$ then the [[Solution to Linear System of Equations|solutions]] of $EA\underline{x}=\underline{0}$ are identical to the solutions of $A\underline{x}=\underline{0}.$ **Proof**: Follows directly from [[Elementary Row Operations Preserve Kernel of Left Multiplication Linear Map of Real Matrix]]. **Proof**: Follows from [[Elementary Row Operations do not Alter Set of Solutions to Linear System of Equations]].