> [!Definition] Definiton (Solution) > A solution to a [[Linear System of Equations|linear system]] is a [[Real n-Space|real vector]] that satisfies all equations in the set. Equivalently if $(A\mid \underline{b})$ is its [[Augmented Matrix of Linear System of Equations|augmented matrix]], then $\underline{x}\in\mathbb{R}^{n}$ is a solution iff the [[Real Matrix Product|matrix product]] $A\underline{x}=\underline{b}.$