Homogenous Systems

A System Of Equations is homogeneous if all its constants are zero $(\hat{0}\in \mathbb{F})$.

Example:

\[ f(x) = \begin{cases} 0 & x\leq 0 \\ \frac{100-x}{100} & 0\leq x\leq 100 \\ 0 & 100\leq x \end{cases} \] $$\{\begin{array}{rl}& \\ & \text{a+b+c=0}\\ & \text{a-b=0}\\ & \text{a+c=0}\end{array}$$

There is always 1 or infinitely many solutions to this

Theorems

• Homogenous System Trivial Solution Theorem
• Homogenous Non-Trivial Solution Theorem
• Homogenous Equals Zero Solution Theorem