## ABSTRACT

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 $x \in {\mathbb{R}}$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315172309/e112b15c-ee8b-4102-9c2c-0d5caba3f84a/content/inline-math1_1.tif"/> (the symbol “∊ ” means “in”) is the unknown variable and a,  b ∈ R $b \in {\mathbb{R}}$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315172309/e112b15c-ee8b-4102-9c2c-0d5caba3f84a/content/inline-math1_2.tif"/> 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 $x = \frac{b}{a};2$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315172309/e112b15c-ee8b-4102-9c2c-0d5caba3f84a/content/inline-math1_3.tif"/> 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