Inhomogeneous Systems of Equations in n-Space

Abstract

The procedures that we used to solve homogeneous systems of linear equations can be modified to solve systems of equations that are not homogeneous. Once we have any one solution to an inhomogeneous system of linear equations, we will be able to obtain all other solutions just by adding the solutions to the associated homogeneous system of linear equations. In the case of 4-dimensional space, the geometric interpretation of the solution set of a homogeneous system in terms of lines, plane, and hyperplanes through the origin leads to a corresponding description of the solution sets of inhomogeneous systems as lines, planes, and hyperplanes not passing through the origin.