Monday:
- Homework 0 As soon as possible, complete the survey
questions on Homework 0 (available on our gradescope page) and upload
them to gradescope. This will let me learn something about
you, and will allow you to be familiar with gradescope so that
there are no issues with turning in your first assignment.
- Study: Read section 1.1 and start section
1.2.
You
should also review Appendices C and D.
- Do: In section 1.1, do 2a and 3a. (The answers are in
the back of the book.) Also try 7. Note that a parallelogram
is determined by two vectors $\mathbf x$ and $\mathbf y$ as in
Figure 1.1 in the text. Then the midpoint of one diagonal is
$\frac12(\mathbf x+\mathbf y)$. Write the midpoint of the other
diagonal in terms of $\mathbf x$ and $\mathbf y$ and show that
they are the same vector.
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Wednesday:
- Study: Read sections 1.2 and start section 1.3 of the
text. Having a look at Appendices A and B would be helpful.
Also Appendix C on fields might help . But we are going to settle
down and concentrate on the fields like the rationals, the reals,
or later the complex numbers. In fact, unless explicitly stated
otherwise, from this point on, you can assume that
our vector spaces are over either the reals or the complex
numbers.
- Do: In Section 1.2: 15, 16, and 18.
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Friday:
- Study: Read Section 1.3
- Do: In Section 1.3: 3, 19, 23, 28 (Hint: consider #5),
and 30.
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Monday:
- Study: Read section 1.4
- Do: In Section 1.4: 6 (assume $\mathbf F$ does not have
characteristic $2$ here), 14, and 15. You should not turn
in problems 7, 8, and 9, but you should be aware of the results
(and that they are straightforward to prove).
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Wednesday:
- Study: Read section 1.5
- Do: 8 ($\mathbf F$ having characteristic $2$ just means
$1+1=0$. This is an exception to the $\mathbf F=\mathbf Q$, $\mathbf
R$, or $\mathbf C$ rule.), 9, and 19.
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Friday:
- Study: Start Section 1.6
- Do: In Section 1.6: 3b and 11. Recall that there is no
lecture on Monday the 20th. This assignment will be due on
Wednesday before lecture starts
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Monday:
- Study: MLK Day. No Class
- Do:
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Wednesday:
- Study: Finish Section 1.6 and Start Section 2.1. Note
that we are not covering Section 1.7 and you are not responsible for
it.
- Do:
- In Section 1.6: 14, 17, 23, and 33a.
- In Section 2.1: 9abc. (Have a look at 1, but do NOT
turn it in.)
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Thursday (x-hour) :
- Study: Finish Section 2.1 and start Section 2.2. There
is a lot of material in these sections and we will not be able
to cover it all in lecture. So a careful reading is advised.
- Do:
- In Section 2.1: 11, 17 and 27ab. (I also suggest looking at,
but not turning in, 1, 10, and 12.)
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Friday:
- Study: Finish Section 2.2.
- Do:
- In Section 2.2: 4, 8, and 10. (Also problem
5 would be good
practice. The answer is in the back of the text.)
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Monday:
- Study: This will be a challenging week. We have the
Preliminary Exam Thursday, and we have to continue with new
material. (Sorry, that is the "Dartmouth way" with our
compressed quarters.) For today, Read section 2.3.
- Do:
- In Section 2.2: 14 and 17. (For 17, the
proof of the Dimension Theorem may give some useful hints.)
- In Section 2.3: 11, 12, and 13.
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Wednesday:
- Study: Read section 2.4 and study for the Preliminary
Exam tomorrow.
- Do: In Section 2.4: 4 and 6.
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Thursday (x-hour):
- Study: The in class portion of the exam will be held
during our x-hour from 1:20 to 2:10. The take home portion can
be downloaded from gradescope and is due prior to the beginning of
class on Friday (at 2pm). Gradescope will not accept late submissions.
- Do:
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Friday:
- Study: Read section 2.5. We will not cover sections
2.6 and 2.7.
- Do:
- In Section 2.4: 15.
- In Section 2.5: 7a and 10a. You should work, but do not
turn in, 4 and 5 (the
answers are in the back of the text). You might want to think about
10b.
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Monday:
- Study: Read Section 3.1 and start Section 3.2
- Do: No written assignment today. But you still need
to work a bit. You are always
well advised to look carefully at quesiton 1 in Section 3.1 (and in
every section we finish). Especailly have a look at problem 3
(the answers are in the back of the text). Try to work problem
12 using induction, but do not turn it in.
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Wednesday:
- Study: Finish Section 3.2. There is a lot in this
section. Careful reading and review of the lecture would be wise.
There is a lot of computational work in this section as well as
theory. Be sure to work a selction of the parts of problems 1, 2,
4, 5, and 6 where answers are provided in the back of the
text.
- Do: In Section 3.2: 8, 14, 17, and 21. For 21, notice
that if $\operatorname{rank}(A)=m$, then $L_A$ is onto.
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Friday:
- Study: Read Section 3.3. We may not finish all of
Section 3.3 today. We are not covering the Leontief model at the
end of the section.
- Do: In Section 3.3: 5 and 8. It would wise to look at
(but you need not write up)
questions 1, 2, 3, and 4 where the answers are in back of the
text.
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Monday:
- Study: Read Section 3.4. We will only be summarizing this
section in lecture. Therefore, I suggest an extra careful
reading of the material.
- Do: In Section 3.4: 3 and 10. For 10, see Example 4 in
the text. Do not turn in, but you should look at the parts of 1,
2, and 4 that have answers in the back of the text.
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Wednesday:
- Study: Skim Section 4.1. We are not covering the
material on the area of a paralleogram. Read Section 4.2 through
Theorem 4.4.
- Do:
- In Section 4.1: 5 and 7. You should also work, but not turn
in, 2 and 3a.
- In Section 4.2: 6, 12, 23, and 26. (Problem 23 requires
Theorem 4.4.)
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Friday:
- Study: Finish Section 4.2 and read Section 4.3 up to
but NOT including Theorem 4.9 (Cramer's Rule). We are not covering
Cramer's rule in this course. We are not covering Section 4.5 and
will move on to Section 5.1 on Monday.
The review in Section 4.4 could be useful.
- Do:
- In Section 4.2: 25. You should be able to check the
answers to problems 13 to 22 easily using the methods in this
section.
- In Section 4.3: 12, 14, and 15.
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Monday:
- Study: Read Section 5.1 and prepare for the midterm on
Wednesday.
- Do: In Section 5.1, 4bd (for 4b, the characteristic
polynomial is $p(\lambda)=-(\lambda-1)(\lambda-2)(\lambda-3)$),
10.
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Wednesday:
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Thursday (x-hour):
- Study: Finish Section 5.1 and start Section 5.2.
- Do: In Section 5.1: 9ab and 12.
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Friday:
- Study: Finish Section 5.2. We will not cover
Section 5.3. We will also not cover the subsections in Section 5.2
on systems of differential equations or general direct sums.
We may do a little of Section 5.4 and then it will be on to Section 6.1.
- Do: In Section 5.2: 8, 10, 13, and 14. I
suggest looking at problem 12. The
answer is on the web.
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Monday:
- Study: Read Section 5.4
- Do: In Section 5.4: 11, 13, 17, and 19. Naturally, it
would be good to have a look at 1, 2, and 6 (at least those parts
that have answers in the back of the book).
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Wednesday:
- Study: Read Appendix D (on complex numbers) and Section
6.1
- Do: In Section 6.1: 4b, 6, 9, 10, 11, and 16a.
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Friday:
- Study: We will finish most of Section 6.2 today. Please
note that we may be skipping parts of Section 6.2 through 6.6 as we finish
up. You will only be responsible for what we cover in lecture.
- Do: No new written assignment today. However, it would be wise
to work some of the parts of problem 2 (in Section 6.2) that have
answers in the back of the book. You will certainly need to be
able to use the Gram-Schmidt method down the road.
This assignment, Homework number 8, will be the last
assignment to be turned in.
There will be homework assigned, but it will not be graded. Of
course, it goes without saying that that
does not mean that it will not be covered on the final exam.
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Monday:
- Study: Read Section 6.2 and start Section 6.3. We are
not covering least squares approximations and minimal solutions in
Section 6.3.
- Do: In Section 6.2: 7, 8, 11, 17, and 19c.
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Wednesday:
- Study: Finish Section 6.3 and 6.4.
- Do: In Section 6.3: 8, 9, 11, 12, and 13.
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Friday:
- Study: Read the revelant parts of Section 6.5.
- Do:
- In Section 6.4: 2a and 9.
- In Section 6.5: 2abd (in part (d) the characteristic
polynomial is $-(\lambda+2)^2(\lambda-4)$), 3, 10, and 11.
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