- (Section 1.1) Make sure you clearly understand what is
going on in 1-10. Then work out a good selection of 11-16,
17/18, 19/20, 21, 25-27.
- (Section 1.2) Make sure you completely understand 1-4,
13/14, 23/24, 40-42. Solve 15-22 by using the augmented matrix and
Gaussian elimination with back substitution. 25-30, 35/36,
37/38.
Focus problems for the tutorial: 20/22/26/30/36/41
- (Section 1.3) Make sure you understand 1-6 completely and
that you can explain (where appropriate) why a certain
computation is not defined. 7-10 include some good "test"
questions on matrix multiplication. 11-14 is "read and
understand". More good exercises: 15/16, 23/24, 25(important),
26(worth some thought), 27/28. The following are all important
exercises: 29, 30, 33/34, 35, 36.
- (Section 1.4) Do at least one question from each grouping.
5-8. 9/10 (if you are familiar with these functions, the
result, although a certain amount of work, is interesting).
15-18. 19/20, 21/22: important in the future. 23/24 (good test
questions). 25-28: make sure you can do one, but there are
better ways of solving these problems. 31 is a good
"conceptual" or "abstract" exercise. We've solved 32 in class.
33 is important; make sure you understand 34-36 as well.
39/40. 41-48 is a good sequence of theory exercises. 49/50.
Make sure you understand the True/False review at the end.
Focus problems for the tutorial: 6, 22, 24, 26, 31, 33, 50.
-
(Section 1.5) 1-8 are conceptual exercises. Read carefully,
make sure that you understand the questions and how to answer
them. 11-18 are the standard practice exercises for 'find the
inverse of A, if it exists'. Make sure that you are
comfortable with solving this kind of problem. 19-22 use the
same skills for more abstract kinds of problems. You should
understand and be able to do this kind of question. 23-28 are
not so important. They are rather fussy computations of things
that the theorems tell us exist. 29/30 is a good pair of
'abstract' questions. 31-33 are short proofs similar to things
discussed in class. You should be able to do questions of this
type. Review and make sure you completely understand the T/F
exercises
Focus questions: 15, 16, 18, 20, 21, 22, and a proof.
- (Section 1.6) 1-6. Generally, finding the inverse of the
coefficient matrix is not the best way to solve a system of
linear equations. But these do give you some more exercises on
finding matrix inverses. 9-12: see discussion on page 62, with
Example 2. These are not all that important, but still good
for practice on the basic techniques. 13-17 are good
exercises. A test question is not likely to be as big as 17.
Make sure you understand how to do both parts of 18. Make sure
that you understand how to solve 19/20. Actually doing so is a
fair amount of work! The proofs 21-23 are all good exercises.
Make sure you understand the answers to the T/F questions
clearly.
Focus questions: 15/16, 22, 23.
-
(Section 1.7) 1/2 Do you understand all the definitions of this
section? 3-6: Make sure that you understand why multiplication
by a diagonal matrix is easy; 7-10 covers the same ground for
powers of diagonal matrices. 11-16 are more of the same, but
do make sure that you understand why 13/14 are trivial! 17/18
and 25/26: Definition of symmetric matrix. 19-24 are simple
calculations based on the properties we have learned. Do 27/28.
Understand #29! Do all parts of 30. 34.36,39. 41/42 introduce
the concept of antisymmetric matrices, which we may use later.
Do them, and 43, 44, 45 as well. Make sure you know and
understand all the answers to the True/False questions.
Focus questions: 13/14, 16, 28, 30, 32, 37, 39.
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