Row Reduction

Abstract

A linear equation in n unknowns x₁,…,x_n is an equation of the form

$${a_1}{x_1} + {a_2}{x_2} + \ldots + {a_n}{x_n} = b,$$

where a₁,a₂,…,a_n,b are real or complex numbers, and are referred to as the coefficients of the equation. When n = 2 and a₁, a₂ are real, such an equation is the Cartesian equation of a straight line in ℝ² (Fig. 3.1(a)); when n = 3 and a₁ a₂, a₃ are real we have the Cartesian equation of a plane in ℝ³ (Fig. 3.1(b)); see section 1.5(f).