System of Linear Equations

1.1. The General Form of a System of Linear Equations

$$\begin{array}{c}{a}_{11}{x}_1+\cdots +a_{1n}{x}_n=b_1\\ ⋮\\ a_{m1}{x}_1+\cdots +a_{mn}{x}_n=b_m\end{array}$$

where $a_{ij}\in \mathbb{R}$ and $b_i\in \mathbb{R}$.

$x_1,\dots ,x_n$ 는 위 시스템에 대한 unknowns 이다.

위 시스템은 다음과 같은 form 으로 보일 수 있다.

$$\left[\begin{array}{c}{a}_{11}\\ ⋮\\ a_{m1}\end{array}\right]x_1+\left[\begin{array}{c}{a}_{12}\\ ⋮\\ a_{m2}\end{array}\right]x_2+\cdots +\left[\begin{array}{c}{a}_{1n}\\ ⋮\\ a_{mn}\end{array}\right]x_n=\left[\begin{array}{c}{b}_1\\ ⋮\\ b_m\end{array}\right]$$

또는

$$\left[\begin{array}{ccc}{a}_{11}& \cdots & a_{1n}\\ ⋮& & ⋮\\ a_{m1}& \cdots & a_{mn}\end{array}\right]\left[\begin{array}{c}{x}_1\\ ⋮\\ x_n\end{array}\right]=\left[\begin{array}{c}{b}_1\\ ⋮\\ b_m\end{array}\right]$$

2. Related

3. References