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