Solution_to_Simultaneous_Linear_Equations

Let $\displaystyle \forall i \in \closedint 1 m: \sum _{j \mathop = 1}^n {\alpha_{i j} x_j} = \beta_i$ be a system of simultaneous linear equations. where all of $\alpha_1, \ldots, a_n, x_1, \ldots x_n, \beta_i, \ldots, \beta_m$ are elements of a field $K$. Then $x = \tuple {x_1, x_2, \ldots, x_n}$ is a solution of this system $\sqbrk \alpha_{m n} \sqbrk x_{n 1} = \sqbrk \beta_{m 1}$ where $\sqbrk a_{m n}$ is an $m \times n$ matrix.