Spring
2007
MATH 3260 – Linear Algebra
|
Date |
Section |
Assignment |
|
Jan 8 |
Systems
of linear equations and matrices; Gauss elimination. Solution to systems of linear equations. |
Read sections 1.1 and 1.2. Carefully read
all examples. Hw#1 (due
Jan 17): section 1.1: 3c), 11, 12, 14. Section
1.2: 6(a), 10(a), 13(b), 22, 28. |
|
Jan 10 |
Gauss elimination method. See Maple
file. Also, Maple exported as html
file |
Read
about homogeneous systems and their consistency. Suggested
problems: as many as you can from 1.1-1.2 |
|
Jan 15 |
No
classes. |
|
|
Jan 17 |
Matrices
and matrix operations. Maple
file and html
file. |
Read
Section 1.3. Also read the definition of the transpose of a matrix (see page
33). See
html output of the Maple worksheet at left. Check WileyPLUS site. I posted two assignments: one is reading, another one is with some questions. Just try it out to
see how it works. Hw assignment will be posted soon. Hw#2 (due
Jan 24): section 1.3 ex.
6(a, d, e), 13, 22(c), 27, 30. section 1.4 ex. 4(a, b), 6(a), 8, 16. ex 14(a)
supplementary section. (see ex 14 section 1.4 for model in Resources
page) |
|
Jan 22 |
The
inverse of a matrix. (section 1.4) |
Read
Section 1.4 and work your homework. Work as many problems as you need. Quiz on Wednesday (on sections 1.3 and 1.4)! |
|
Jan 24 |
The
algorithm to find the inverse of a matrix. Maple
file. (Html
version). Example done in evening class: maple
file and html
file. |
Hw#2 due. Read section 1.5 and by all means, learn how to multiply
matrices! Suggested problems: work as many as possible. Check WileyPLUS! Look also at the problems in Discussion & Discovery:
22, 23, 24. Hw#3: (due Jan.31): section
1.5: 8(c), 10, 18. Section 1.6: 16,
18, 20, 22(a). Check the updates on WileyPLUS. |
|
Jan 29 |
Solving systems and invertibility
of matrices. |
Read section 1.6 and pay attention to the examples. Here is
a hint for pb 18 on Hw#3. |
|
Jan 31 |
More on
invertibility of matrices. Diagonal, triangular and
symmetric matrices. (section 1.7) |
Hw#3
due. Hw#4: (due Feb. 7) Section 1.7: 11(a,b), 22(a), 18, 30(a). Supplementary pb:
7, 15. Section 2.1: 2(b), 6, 12, 16, 18. Note:
Remember you have to show your work in hw to receive full credit for a
correct answer. Suggested
problems: section 1.7: 7, 9, 12, 19, 20. Updates on Wiley coming soon! |
|
Feb 5 |
Chapter
2: Evaluating determinants by the cofactor expansion.(2.1) |
Check
the link to the free download SAGE
(it works for linear algebra) program. |
|
Feb 7 |
Evaluating
determinants by row reduction. Properties of determinants. (2.2 & 2.3) |
Hw#4 due |
|
Feb 12 |
Review and more applications of determinants: eigenvalues. |
Suggested
problems: as many as you can from 2.2, 2.3. Hw#5:
section 2.2: 4,6, 9 (you don’t have to reduce the matrix to row-echelon
form in any of these exercises),14(a), 19. section
2.3: 2, 4(b), 5, 12(b), 15(for ex. 14b). to be
continued Hw#5 is
due Feb. 19. |
|
Feb 14 |
Exam #1: Chapters 1 & 2(2.1-2.3) See Practice
exam on Resources
page. The answer key
to practice is there as well. |
|
|
Feb 19 |
Vectors
in 2 and 3 dimensions. Introduction, operations with vectors. (3.1) |
Hw#6:Section 3.1: 5, 9, 10, 20,
21(e); Section 3.2: 6, 7, To be
continued… |
|
Feb 21 |
Norm of
a vector. Dot product. (3.2, 3.3)
|
See
updates on WileyPLUS. You may need to practice more
than just Hw. Hw#6:Section 3.1: 5, 9, 10, 20,
21(e); Section 3.2: 6, 7, 10 (write a
justification for part a). Section 3.3: 2(for part d) of ex
1), 13, 16(d). Think
about:16, 17 (3.2) 19, 25, 27, 29, 31 (3.3). |
|
Feb 26 |
Orthogonal
projection of a vector on another vector. Distance from a point to a
line.(still 3.3) The
point-normal equation of a plane. (3.5) |
Quiz on 3.1-3.3 what we covered so far Hw#6 due Assignment: Read 3.3 (pg 140-142) Read 3.5: pg 156-159. Suggested problems: 3.3: 5, 6, 12, 13, 14, 17, 18. Hw#7:(J due March 12) section 3.3:
6(d), 17(a). Section 3.5: 4, 5(b), 6(a), 7(a),
8(b), 9(b, d), 10(a), 11(a), to be continued… |
|
Feb 28 |
More on planes and lines in a 3-space. Evening class meets in SC 212 |
Check
the Resources page for some hints on how to solve
problems in 3.5 and some solved problems. Read 3.5,
including the distance between a point and a plane formula. See
updated Hw#7: :(J due March 12) Section 3.3: 6(d), 17(a). Section 3.5: 4, 5(b), 6(a), 7(a), 8(b),
9(b, d), 10(a), 11(a), 22, 35, 39 (a).
|
|
March 3-March 9 |
Have a wonderful Spring Break! |
A
practice exam for Exam 2 is now posted on the Resources page. Do not worry, the day of the exam is still to be decided. |
|
March 12 |
Euclidean
Vector Spaces ( |
Hw#7 due. Read
section 4.1. Hw#8: Section 4.1: 3, 4, 10, 18(b), 20,
21, 22, 37(a,b,c). Section 4.2: 2(b,c), 4(c,d), 8(c), 18(b,c). Section 4.3: 3, 6(b), 8(a,b),
10(b), 18(b) removed!! See update below! Do not
work the problems ahead. Wait until we cover the theory. |
|
March 14 |
Linear transformations from Properties of linear transformations. |
Quiz on
3.5 and 4.1. You are allowed to bring a formula sheet with a “survival kit”.
The sheet should not have examples or worked problems. Suggested
problems: section 4.2: 5, 6, 10, 11, 17, 20, 22. |
|
March 17 |
I will offer a review session If no entrance is open, the door at the end of
the hall where the room is will be open. |
|
|
March 19 |
More on properties of linear transformations. |
Check WileyPLUS site for updates. Suggested
problems on section 4.3: as many as you can.
The sky is the limit. Update
on Hw#8 Section 4.3: 3, 5 (a), 6(b), 7(c, d)(write the matrix of
the transformation and check if the transformation is 1-1 using Thm4.3.4 then
find the inverse), see file for additional problem! |
|
March 21 |
Exam #2: Chapter 3 (skip 3.4), 4.1-4.3(no eigenvalues,
no problems using Thm. 4.3.2 or 4.3.3). You are allowed a formula sheet but it may
not contain examples, worked problems or proofs. |
Hw#8 due Spring is here
|
|
March 26 |
More on linear transformations. Ono-to-one and onto
transformations between different Euclidean vector spaces. |
Read Thm. 4.3.2, 4.3.3, and about eigenvalues
and eigenvectors for a linear transformation. See examples 7and 8 in section
4.3. Hw#9: Section 4.3: 8(a, b), 10(a,b), 16(b, c), 28. to be continued… |
|
March 28 |
Chapter
5: Real Vector Spaces |
More on
Hw#9: Section 5.1: 1, 5, 6, 10,
17(a). Note: if the space is not a vector space it is enough to identify ONE
axiom that fails not all of them as it is required in the text. Notice a change in the assignment! If you
used WileyPLUS this semester, please take a few
moments of your time to complete their survey.
Thank you! A new
assignment is now posted on WileyPLUS. Enjoy your
weekend but do practice as well! |
|
April 2nd |
Real
Vector Spaces. Subspaces. |
Read
Section 5.2: pages 229-234(up to the definition of a linear combination of
vectors). Pay attention to examples. |
|
April 4 |
Linear
combinations of vectors. The subspace spanned by a set of vectors. |
Hw#9 due. Quiz on 4.3, 5.1 and 5.2 Suggested
problems: 5.2: 1, 2, 3, 4, 6. Hw#10: 5.2: 2(a,b),
3(b,c), 6(a, b, c), 8(a), 9(a), 11(a, c). See this for some more
examples on problems in 5.2. |
|
April 9 |
Linear
independence. |
Hw#10 due (it is a short homework!!) |
|
April 10 |
Services for
Valerie Antranikian are at Roswell Funeral Home.
950, If you
would like to make any donations to Valerie’s memory, I am collecting from
Math/Stats majors. Also, I have a card in my office if you would like to
sign.
|
|
|
April 11 |
Basis
and dimension. |
Suggested
problems: 5.3: 2, 3, 4, 5, 8, 9, 18. Hw#11: due
April 18 Section
5.3: 6(a), 8, 9. Section
5.4: 4(b), 7(b), 9(a), 14, 18(a,c) to be
continued. |
|
April 16 |
Row
space, Column space and Nullspace of a matrix.
(section 5.5) Maple file on finding the row space, column space and nullspace of a matrix. Same file exported as html file. |
Quiz on
5.3 & 5.4. Hw#11: continued
from above: section 5.5: 3(c), 6(c), 11(b). Check
this link for
more sample problems solved on 5.5 and 5.6. Check
the Resources page for the practice test. |
|
April 18 |
Rank
and nullity. (section 5.6) Maple file on rank of a
matrix. |
Hw#11 due Solutions to Hw#10 are now posted. Updates
on WileyPLUS were made. You can check the site for
more practice problems. Solutions to Practice 3
are now posted on the Resources page. Suggested
problems on 5.6: 2, 4, 7, 9. Supplementary
problems: 1, 2. |
|
April 20 |
Review session in CL
2005 from 9-11 am. |
Solutions to Hw#11 (Maple exported as
html file). You can see the Maple file as well. Have a
good weekend! |
|
April 23 |
Exam #3: covers 4.3 and everything
we did in chapter 5 (5.1-5.6) |
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April 25 |
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April 26 |
|
I am
going to be in my office in the morning, until probably I will
have a student here at 9 staying probably until 11 but if you need to ask
questions stop by. On
Friday I will be available after |
|
April 29 |
Review in
CL 1005, 10-12. |
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