chapter  1
14 Pages

## Vectors and linear systems

ByQingwen Hu

A central goal of linear algebra is to solve systems of linear equations. We have seen the simplest linear equation ax = b, where x ∈ R $x \in {\mathbb{R}}$ (the symbol “∊ ” means “in”) is the unknown variable and a,  b ∈ R $b \in {\mathbb{R}}$ are constants. It is known that there are three scenarios for the solutions: 1) if a ≠ 0, there is a unique solution x = b a ; 2 $x = \frac{b}{a};2$ 2) if a = 0,  b ≠ 0, there is no solution; 3) if a = b = 0, there are infinitely many solutions. We are then motivated to investigate systems of equations with multiple unknown variables. The following system