A Few Matrix Applications

Solving Systems of Linear Equations Using Matrices. A system of linear equations can be written compactly as a matrix equation:

$Ax = b$

Here, $A$ is a matrix of coefficients, $x$ is a vector of variables, and $b$ is the result vector.

There are several ways to solve this system:

1. Gaussian elimination: Transform the augmented matrix $[A | b]$ into row-echelon form.
2. Matrix inverse (if $A$ is invertible): $x = A^{-1}b$.