Sections 1.1 – 1.4 (see syllabus table for day by day breakdown).
There are lots of very short exercises at the end of the section that will help you figure out whether you have mastered the ideas of the section. Try spending an hour doing as many of the odd-numbered problems 1-33 as you can, checking the answers in the back AFTER you have given your own answer. Some of these are very quick (e.g., what systems are linear in 1 - 5).
Picky but Very Important: Write down the systems in 7 and 9 and pay attention to the difference in position between a12 and a21. In 7 for example, is the first row of the matrix 1 3 or 1 4. This is a very important convention on the order of the indices.
Solve it! Save time to actually solve at least a couple of 31, 33, 35. Be sure to get good matrix practice by writing down the matrix and practicing matrix tools and not by operating on the equations.
Words: One important point in this section is to understand the terminology echelon form and reduced echelon form and the difference between them. Look for this in practicing on a few of the odd problems 1-9.
Solutions from Augmented Matrices (no computation needed): This is so important that you should do all the problems 11, 13, 15, 17, 19, 21. The good news is that no calculation is required, but the practice is really needed to cover all the kinds of cases.
Solutions (computation needed): You really need to practice on some of the odd problems 23-35, but you probably do not have time for all of them. Use matrix methods. Try at least one of the hairier ones. Think about what is going on and look for patterns and insights as well as the answers.
Two problems to challenge your row operating: Try 37 and 39. If your operation is R1 + kR2, what is k?
What can happen? In the odd problems 7-21, write down clearly what can happen and then check your answers.
One or more examples will be shown in class. There will be more about this next week.
(SHOW YOUR WORK)
1. Section 1.1, Problem 38
2. Section 1.2, Problem 40
3. Section 1.2, Problem 49
4. Section 1.2, Problem 50
5. Section 1.3, Problem 2 (by hand)
6. Section 1.3, Problem 4 (by hand)
7. Section 1.3, Problem 24 (by hand)