Study guide and 10 practice problems on:

## Linear equations

To analyze a system of linear equations, it is convenient to put it into the matrix form $$\mathbf{A} \mathbf{x} = \mathbf{b},$$ where $\mathbf{A}$ is a known matrix, $\mathbf{b}$ is a known column vector, and $\mathbf{x}$ is a column vector of unknowns.
If $\bfA$ is square and invertible, the solution to $\bfA \bfx = \bfb$ is $\bfx = \bfA^{-1} \bfb.$
If $\mathbf{b}=0$, then the equation is called homogeneous.
If $\mathbf{b} \neq 0$, then the equation is called inhomogeneous.