Study guide and 3 practice problems on:

## Homogeneous linear equations

Let $\mathbf{A}$ be an $n \times n$ matrix. Linear equations of the form $\mathbf{A} x = 0$ are called homogeneous.
If $\text{ det } \mathbf{A} \neq 0$ then $\mathbf{A} x = 0$ has exactly one solution, $x=0$. If $\text{ det } \mathbf{A} = 0$ then $\mathbf{A} x = 0$ has infinitely many solutions.