II. System of Non-Homogeneous Linear Equations Coefficient Matrix Matrix form Of equations Guiding system （1）（1）

Determine solutions of nonhomogeneous system Use Vectors Vector equation of the system System (1) has solutions Methods to solve nonhomogeneous system 1. Properties of nonhomogeneouse system’s solutions

Property 1: The margin of two solutions of system (1) is a solution of guiding system. Property 2 ： The sum of a solution of nonhomogeneous system(1) and a solution of guiding system is a solution of nonhomogeneous system(1). 2. General solution of nomhomogeneous system Then general solution of system (1) is Theory : Deduction General solution is

e.g.1. Solve the system Has solutions Equivalent system

So, the fundamental system is General Solution :

e.g.2. Find the general solution. Equivalent system Has solutions

the fundamental system is Process of solving homogeneous system How to determine ？ What to note ？

System with parameters We should determine the parameters before solving the system.—this is obligatory.To determine the parameters, the following form should be satisfied. Generally, we have two ways. First we can use determinant Second we can use elementary operations. Completement

The system has no parameters any more. The system has no parameters any more.

Question : Can we solve it by determinant? No ！

Two questions about the system. For the hypothesis, there is only one solution vector in the fundamental solution system which is （ please look at it in reference page 82 ）