> [!summary] The solution set is the solutions for a set of unknown variables in a linear equation. >[!info]+ Read Time **⏱ 1 min** # Definition A solution is a [[Sets|set]] of solutions for a [[Sets|set]] of [[Linear Equations|linear equations]]. It is the solution for each unknown variable. The notion of a solution set is a [[Scalar & Vectors|vector]] $\vec{s}$ in $\mathbb{R}^n$ whose variables ($s_{i}$) is the solutions of unknown variables in a linear equation ($x_{i}$) for $1\leq i\leq n$. $ \vec{s} = \begin{bmatrix} s_{i_{1}} \\ \vdots \\ s_{n} \end{bmatrix} \in R^n $