Page 28 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Figure 1.2.1

There is one case in which a homogeneous system is assured of having nontrivial solutions—namely, whenever the system involves
more unknowns than equations. To see why, consider the following example of four equations in five unknowns.

EXAMPLE 7 Gauss–Jordan Elimination
Solve the following homogeneous system of linear equations by using Gauss–Jordan elimination.

(1)

Solution

The augmented matrix for the system is

Reducing this matrix to reduced row-echelon form, we obtain

The corresponding system of equations is