SystemsOfEquationsGaussianElimination

# Solutions of a system

A **solution of the system** is a solution of all the equations.

Examples:

**To solve a system**is to find all of its solutions.

Depending on the number of solutions, we can classify the systems:

–Consistent systems: if there is at least one solution. They can be:

· Independent systems: there is one solution

· Dependent systems: there are infinite solutions

–Inconsistent systems: if there is no solution

Examples:

NOTE#1: A homogeneous system has always a solution.

A **degenerate equation** has the form:

0x_{1} + 0x_{2} + ….. + 0x_{n} = b

Then:

–If b = 0, it is called **trivial equation**

–If b ≠ 0, it is called **absurd equation**

NOTE#2: if there is an absurd equation in a system then it is an inconsistent system

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