Linear System

A system of Linear Equations.

Representation

There are several equivalent ways to represent a linear system.

A system of Equations

$$\begin{array}{rl}2x+3y& =7\\ x-y& =5\end{array}$$

An Augmented Matrix

$$\left[\begin{array}{ccc}2& 3& 7\\ 1& -1& 5\end{array}\right]$$

A Vector Equation

$$x\left[\begin{array}{c}2\\ 1\end{array}\right]+y\left[\begin{array}{c}3\\ -1\end{array}\right]=\left[\begin{array}{c}7\\ 5\end{array}\right]$$

A Matrix Equation

$$\left[\begin{array}{cc}2& 3\\ 1& -1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}7\\ 5\end{array}\right]$$