1. Guassian Elimination is really just using the regular Elimination Method and applying the Triangular Form procedures to a set of linear equations, but without having to write down all the variables in the equations each time. This in itself simplifies the procedure and helps focus on the task. What is the ultimate goal of all these methods and procedures?
2. If you had 5 linear equations using 5 variables, what would the augmented matrix look like? What would this matrix look like in echelon form?
3. What does the final row of the augmented matrix in echelon form (the above description) tell you about the solution to the system of 5 linear equations?
4. Is it always possible to take any square matrix and write it in echelon form with all 1's along its main diagonal?
5. Can you take any two matrices and add them, subtract them and multiply them together?
6. Is it possible to divide two matrices?
This explains how matrices are used to solve equations, and also explains matrix operations.