Homogeneous System of Linear Equations

Definition: Homogeneous System of Linear Equations

A system of linear equations is homogeneous if the right-hand sides of all equations are $0$, i.e. the system’s augmented matrix is $(A\mid \vec{0})$:

$$\left[\begin{array}{cccc}{a}_{11}& \cdots & a_{1n}& 0\\ ⋮& \ddots & ⋮& ⋮\\ a_{m1}& \cdots & a_{mn}& 0\end{array}\right]$$