# Homogeneous Systems

If a **system** of * m* equations and

*unknowns has all zero independent terms, it is said to be*

**n****homogeneous**.

It only admits the trivial solution**:** **x _{1} = x_{2 }=... = x_{n }= 0.**

The necessary and sufficient condition for a homogeneous system has solutions other than the trivial when the rank of the coefficient matrix is less than the number of unknowns, that is to say, that the determinant of the coefficient matrix is zero.

r < n

### Solving Homogeneous Systems

r = 3 n = 3

r = 3 n = 3