Study guide and 2 practice problems on:

## Inhomogeneous linear equations

Let $\mathbf{A}$ be an $n \times n$ matrix. Linear equations of the form $\mathbf{A} x = b$ are called inhomogeneous if $b \neq 0$.
If $\text{ det } \mathbf{A} \neq 0$ then $\mathbf{A} x = b$ has exactly one solution, $x=\mathbf{A}^{-1} b$. If $\text{ det } \mathbf{A} = 0$ then $\mathbf{A} x = b$ has either no solutions or infinitely many solutions.