# Introduction to linear equations and matrices

In this free course, matrices are used as a concise way of representing systems of linear equations, which occur frequently in mathematics.

# Learning outcomes

- Use the method of Gauss-Jordan elimination to find the solutions of systems of simultaneous linear equations.
- Solve a system of linear equations by row-reducing its augmented form.
- Perform the matrix operations of addition, multiplication and transposition and express a system of simultaneous linear equations in matrix form.
- Determine whether or not a given matrix is invertible and if it is, find its inverse.
- Evaluate the determinant of a 2 x 2 or 3 x 3 matrix and use the determinant to determine whether or not a given 2 x 2 matrix is invertible.