Linear System

A System Of Equations with $n$ equations in $k$ variables $x_1,x_2\dots ,xk$ in the form:

$$\text{empheqlbrace}\begin{array}{rlrlrlr}{a}_{11}{x}_1& +& a_{12}{x}_2& +\cdots +& a_{1n}{x}_n& =& b_1\\ a_{21}{x}_1& +& a_{22}{x}_2& +\cdots +& a_{2n}{x}_n& =& b_2\\ \dots & & & & & & \\ a_{j1}{x}_1& +& a_{j2}{x}_2& +\cdots +& a_{jn}{x}_n& =& b_j\end{array}$$

Where the entries $a_{jk}\in \mathbb{F}$ and the values $b_j\in \mathbb{F}$

The solution to this linear system is are the values that satisfy each equation.

• 1 solution means the system is indep
• infinite solutions means the system is dep