# Week 5

## Topics

The next two weeks are devoted to solving systems of linear equations. Linear
equations come up all the time in real life. Solving them is not hard in principle,
but tedious. Computers were invented mainly
to solve linear equations.

We will look at a total of six different ways to solve systems of linear equations:

- The Graphical method
- The Substitution method
- The Elimination method
- The Augmented Matrix method
- The Inverse Matrix method (next week)
- Using Excel (in two weeks)

The graphical method only works for systems of two variables. We will restrict
ourselves to two variables for the other hand-calculation methods as well.
If you can do it for two equations, you can do it for three or four, it just
takes longer.

This week, we will cover sections 4-1 and 4-2, which include the first four
of the methods mentioned above. Specifically, we will look at

**Chapter 4-1**** **: Systems
of Linear Equations (background and first 3 methods)
**Chapter 4-2**** **: The
Augmented Matrix method

We will skip section 4-3. If you scan this section, it appears that they are
covering yet another method called Gauss-Jordan Elimination. This method is
the same as the Augmented Matrix method. So why do they give it a new name?
Ask the authors. Mainly, they are doing bigger problems in this section, and
explaining the degenerate cases in more detail (no solution or infinitely many
solutions).

## Assignments

Read the textbook and do the homework assignment HW 4.

**Note:** a couple of the problems say "solve by Gauss-Jordan Elimination". Just ignore that, and solve the equations by whatever method you prefer.

Last Updated:
Wednesday, August 5, 2015