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(Section 3.1) Questions 1-16 are sometimes quite simple
exercises on the definitions of the basic concepts of this
section, and often relate directly back to things that we
learned about matrix algebra. Exercises 17-22 involve solving
simple systems of linear equations. The remaining exercises
explore various simple aspects of geometry, as interpreted
through vectors.
The proof questions duplicate work we have already done in
parts of Chapter 1. You should find them all straightforward.
Make sure that you know and
understand all the answers to the True/False questions.
Focus questions: 4(a), 6(a), 8(b), 15, 16, 23, 29.
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(Section 3.2)
(For the quizzes, March04/07): Computational problems like
1-10. Conceptual questions like 15/16. Proofs like 33-35.
And in addition, for the next lab: 11-14, 19/20,
26/27, 29/30. 28 is a good, but challenging, question!
Make sure that you know and
understand all the answers to the True/False questions.
Focus questions: 2(b), 3(d), 6(a), 8, 10(b), 16
and then 12, 19, 26, 27, 29
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(Section 3.3)
1/2 simple computations. 3-6, 7-10, 11/12, 13/14 are all
basic skills, and 13/14, 15-20 are standard test questions.
Distance questions 21-24, 25/26, 27/28 are important. 29-34
on orthogonality and projections also provide good test
questions. 34-37 are physics/engineering questions and are
important to students in those subject areas.
Always try the proofs (38/39).
Make sure that you know and
understand all the answers to the True/False questions.
Focus questions: 20, 24, 26, 29, 32, 34.
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(Section 3.4)
1-12 are straightforward questions on the application of the
formulas learned in this section. 13-16 are more typical of
test questions; they require you to think for a moment or
two before answering. 17-20: as I said in class, I generally
do not like questions which say 'Do some computations and
verify that the results agree with a theorem'. 21-24 ask you
to think about the connections between solutions to systems
of linear equations and the geometry we have been studying
in this section. Make sure you understand this. 25-28 deal
with key ideas, with 27/28 being more typical of a test
question. 29 can be omitted for now: it is a question that
makes connections with the material we will be studying in
1.8/4.9.
Make sure that you know and
understand all the answers to the True/False questions.
Focus questions: 13-16, 23/24, 27/28
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(Section 3.5)
1-8 are all important but quite basic computational
questions. 9-18: You need to remember and to be able to use
the area and volume formulas needed to answer these
problems. 19-20 is another basic application of this
section. 21-24 are basic computational exercises. 25-26 are
computations that test understanding of the theory. We like
to ask this kind of question. 27/28 are a couple of more
applications in geometry. 29/30 are two good 'manipulation'
or 'theory' problems. Omit 31/32
Proofs : 33-37; 40 gives an alternative to and maybe easier
to understand proof of 3.5.1(d) than the one we did in
class, 41 suggests a really easy proof of 3.5.1(e) once we
have done 3.5.1(d) by either method;
42 is a good exercise too.
Make sure that you know and
understand all the answers to the True/False questions.
Focus questions: I won't mention any particular parts of 1-8
but you do need to be able to do these sorts of computations;
and the same commebnt for 9-18. 25/26 are important, as are
29/30. In the proofs: 34(a), 37, 40, 42(b)
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(Chapter 3. Supplementary exercises)
1/2/3 are straightforward computational exercises, but the
rest are more interesting. 4 is an important test of your
understanding of the material of this chapter. 5-21 explore
many different ways that we can ask you questions about
linear algebra and geometry. You should understand how to
solve all of these problems;
some of them require two or three different steps using
different parts of the theory. 19/20 are good exercises.
22-25 are all good too, but 24 needs to be modified:
24. Find several different examples to show that the
statement given is false. Come up with a simple correction
(one important additional word!) to make it true, and prove
this version.
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