## Reading

For this assignment you should read Chapter 1, Sections I, II, and III. There is a lot of material in there, and I think it would be most helpful to follow all of the examples. This reading (and your notes from class) should help you complete your first assignment.

There are a few chucks of these sections that you should feel free to skim through or skip all together. In particular, I recommend doing this starting at the bottom of page 26 (at the word “proof”), and ending towards the end of page 27 (at the phrase “QED”). I also recommend skipping the proof of Lemma 3.7 and, instead, focusing on relating that result to Examples 3.8 and 3.9.

## Assignment 1

Problem 1. Write down the (augmented) matrix that represents the system of equations

Is this a homogeneous system? Why or why not?

Problem 2. What does it mean to say that a system is *inconsistent*? Explain whether or not it is possible for a homogeneous system to be inconsistent.

Problem 3. Solve the system of equations that corresponds to the augmented matrix

.

Problem 4. Solve the system of equations that corresponds to the augmented matrix

.

Problem 5. Compare your answers to Problems 3 and 4 to the prediction made by Lemma 3.7 (pg. 27). Can your solution set for Problem 4 be written according to this result? If so, do it! If not, um, spoiler alert, but you’ve made a mistake!

Problem 6. What is a *leading variable* in a system of equations? What is a *free variable*?

Problem 7. Complete Problem 2.18(e) (pg. 20).

Problem 8. Complete Problem 2.22(a) (pg. 21)

Problem 9. Complete Problem 3.16(a) (pg. 33)

Problem 10. 3.19 (pg. 33)