Math 308 Week 4 Assignments
Reading for this week and up to the Midterm
This week we begin Chapter 3. Roughly the classes will correspond to these
sections:
- Wed 10/18: (Subspaces) Sections 3.1, 3.2 and part of 3.3 (especially
Theorem 4 about null space of A)
- Friday 10/20: (Subpaces associated with a matrix) Rest of Section
3.3, perhaps a little of 3.4
- Monday 10/23: (Bases) Section 3.4
- Wednesday 10/25: (Bases and a bit of dimension) Section 3.4 and certain
pages in 3.5 to be announced.
Note: Midterm is Friday 10/27. There will be a further explanation
of what will be on the midterm in a separate document.
Note about Chapter 2: As has been pointed out, this chapter presents
prerequisite material about vectors, lines, planes, etc in 2-space and 3-space
that is taught in Math 126. So you have seen this material before. This material
will supply many examples and problems in the more general theory in Chapter
3, so the better you know it, the better you will understand Chapter 3 (though
Chapter 3 may shed some light on Chapter 2 also). Anyway, it is expected that
you can handle examples in 2-space and 3-space. If you have questions or need
help with material in Chapter 2, you are welcome to ask.
Practice Problems (not to be turned in)
For Friday 10/20
- Section 3.1: Study quickly the problems 12-30. Pay special attention
to the NOTATION used in 12-21 (and in the text). This is the
set-theoretic notation that is called for in problems 22-30. In other words,
in problems 12-21 you make the description look something like the one in
22-30 and then vice-versa.
- Section 3.2: Consider carefully the Exercises 1 - 18. You
should be able to deal with most of these without a lot of checking by noting
that the set is the solution space of linear equation (homogeneous or nonhomogeneous).
Compare this with the result in Theorem 4. Also try 23, 25, 29
- Section 3.3: Do 23, 25
For Monday 10/23
- Section 3.3: Exercises 1-20 and 27-37 (odd). At least some
of each type.
- Conceptual Exercises, page 268: 1 through 4 (all)
For Wednesday 10/25
- Section 3.4: Exercises 1-7 (odd) and 11-15 (odd).
- Conceptual Exercises, page 268: 5 - 8 (all)
Written Assignment #4 (due Wed 10/25 at the beginning of class)
Section 3.3
- Problems 20 (parts a, b, c d) and 34 (Note: by algebraic specification,
the authors seem to mean in the form of the answers to Example 2 for the nullspace
and Example 4 for the range). We will discuss other possible language in class
prior to the midterm.
Section 3.4
End of Chapter, Page 266, Supplementary Problems