Spring 2008

MATH 3260 Linear Algebra

 

Date

Section

Assignment

Jan 7

Systems of linear equations and their solvability.

Solving systems with Maple.(Classic worksheet file)

 

Suggested problems: Section 1.1: 1-6; 7, 13, 15, 17, 21, 43, 55, 61, 62, 67, 68, 69, 70, 71, 72, 73. (not a hw assignment) 

Read section 1.1.

See class notes on the last problem in class.

Jan 9

Gauss and Gauss-Jordan elimination methods (section 1.2) Gauss elimination and Gauss-Jordan elimination. (Maple file)

Read section 1.2.

Hw#1 due Jan 16: section 1.1: 72, 73.

                         section 1.2: 27, 30, 36(use Maple to solve this problem), 40, 43, 57; section 1.3: 13, 21.

Suggested problems: as many as you can from 1.2

Jan 14

Class meets in CL 1003

Applications of systems of linear equations.

Read section 1.3.

Suggested problems: section 1.3: 9, 10, 11, 13, 21, 23, 27.

Do not neglect the Chapter review problems: 7, 27, 49,

Jan 16

Operations with matrices.

Maple file on matrices (.mws file); (.mw file)

Hw#1 due

Read section 2.1.

Suggested problems: 5,6, 7, 9, 11, 13, 18, 21, 25, 27, 33, 37, 39.

Jan 17

Information meeting on study abroad in China

1-2pm: see flyer

 

Jan 23

Room change: class meets in CL 1003

Matrix multiplication. The inverse of a matrix.

Solutions to hw#1 are now posted on Resources page.

Solutions to Quiz 1 are posted on Resources page.

Jan 24

Information meeting on study abroad in China

1-2pm in CL 1009: see flyer

 

Jan 28

Elementary matrices.

Notice new problems added to the Hw assignment and to the suggested problems list.

Read sections 2.2 and 2.3.

Suggested problems: 2.2: 7, 11, 17, 18, 23, 24, 25, 29, 30, 32, 33, 35, 36, 41, 53, 54, 55, 57, 59. Note that ex. 53, 59 involve proofs. Do try them but do not despair if you cannot do them at this time. 

Section 2.3: 1, 3, 31, 32, 45, 46, 48.

Hw#2: due Jan 30 section 2.2: 35, 44, 60.

                          section 2.3: , 26(a), 27(b), 36, 38, 46.

Jan 30

More on elementary matrices. The LU factorization. (Ch 2.4)

Read section 2.4.

Suggested problems: 2.4: 1, 2, 5, 9, 11, 16, 19, 21, 25, 29, 30, 39, 45, 48, 51, 55.

Feb 4

Determinants (3.1 and 3.2)

Read sections 3.1 and 3.2.

Suggested pb.:3.1: 1, 5, 9, 11, 13, 14, 15, 16, 19, 20, 21, 22, 33, 49, 50, 51.                 3.2: 1, 3, 5, 5, 7, 8, 9, 10, 21, 23, 25, 26, 31, 32, 33, 34, 35, 36, 37.

Hw#3: due Feb. 11: 3.1: 52.

                            3.2: 20, 24, 28.

                            3.3: 20, 24, 36, 39.      

Feb 6

Properties of determinants. (3.3)

 

Feb 8

Review for Exam in CL 2005: 9-10AM

Hw2 solutions

Feb 11

Exam #1

List of review topics for exam.

Hw#3 due

Feb 13

Introduction to eigenvalues (3.4). The adjoint of a matrix and finding the determinant (3.5)                                                                          

Read pages 152-160.

Suggested problems: 3.4: 1, 3, 5, 6, 11, 12.

        Section 3.5: 1, 3, 9, 10, 11, 12, 17, 25, 27. 

Hw#4 due Feb. 20: 3.4: 6, 8; section 3.5: 5, 10, 27(you may use Maple or a calculator to compute the determinants in pb 27), 37; review problems: 45.

Feb 18

Cramer’s Rule.

Introduction to vector spaces: Chapter 4

Solutions to exam1(green version), (white version)

Read ch 4: 174-183.

Suggested pb: page 164: 17, 25, 31; page 168: 43, 44, 45.

Page 183: 1, 2, 9, 15, 17, 21, 33, 35, 43, 44, 49, 50, 51, 52.

Feb 20

Vector Spaces (4.2)

Read 4.2.

Suggested problems: section 4.2: 17, 19, 20, 21, 23, 25, 26, 29, 30.

Feb 25

Problems on vector spaces.

See some class notes with problems from the book.

Hw#5: due March 12: section 4.2: 23, 25 (b), 28, 29. More to come  

Feb 27

Subspaces of a vector space

 

March

1-7

Spring break

I posted some practice problems for Exam 2 on the Resources page. More problems to come.

March 10

More on subspaces. Spanning sets.

Hw#5: due March 12: section 4.2: 23, 25 (b), 28, 29.

                              Section 4.3: 2, 3, 13, (e), 16, 17, 26.

Suggested problems: 4.3: 1-4; 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 23, 25, 26.

March 12

Quiz on 4.3 and 4.4.

Linear independence and dependence

Read 4.4: through page 206.

The practice test has been updated.

Suggested problems: 1, 5, 7, 9, 10, 11, 13, 35, 38, 41.

Hw#5: due

March 17

Exam review

Hw5 solutions are now posted on the Resources page. So is hw3.

March 19

Exam #2: section 3.4 through 4.4.

You are allowed a formula sheet, but do not bring practice test solutions or hw solutions or any such materials.

March 24

Basis and dimension (section 4.5)

Read 4.5

Suggested problems: section 4.5: 1-4, 5, 6, 7, 8, 11, 13, 19, 21, 25, 29, 33, 39, 40, 41, 42, 43, 49, 51, 52, 53, 56.

Hw#6: due March 31st: section 4.5: 33, 35, 43, 56.

Section 4.6: 6, 9, 12(work with technology is strongly recommended), 15, 23.  

March 26

Quiz on 4.5

 

March 31

4.6: Rank of a matrix and systems of linear equations

Read 4.6.

Suggested pb: 4.6: 27, 33, 35, 43, 51.

Check WebCT tomorrow. I may post some notes.

April 2nd

Coordinates and change of basis

See class notes. Please do read them!

Read section 4.7.

Solutions to quizzes 5 and 6 are posted on the Additional Resources page.

Suggested problems: section 4.7: 3,5,7,8,9,11,13,15,17,25.

April 7

Change of basis. Applications of vector spaces to differential equations.

Read Scetion 4.7 and 4.8 pages 255-258

Suggested problems: 4.8 1, 3, 9, 11, 12, 13, 15, 17, 19, 22, 23.

Review Ch4: 15, 17, 25, 29, 37, 42, 49, 51, 67, 69. 

April 9

Linear Transformations (Chapter 6)

Read 6.1

Suggested problems: 1, 2, 3, 7, 8, 9, 11, 13, 15, 19, 20, 21, 24, 25.

Practice for Exam 3 (with solutions) posted on Additional Resources page.

April 14

One-to-one transformations and range of a linear transformation.

Read section 6.2: pages 365-370.

Suggested problems: section 6.2: 1-6, 7, 9, 11, 39 (see pb 4 done in class for comparison) 

April 16

Exam 3: section 4.4-4.8; 6.1-6.2:only what was covered in class

You are allowed a formula sheet, but no examples or worked problems on it.

Solutions to Hw6 are now posted. You may also see Maple file with work on some problems in Hw6.

A few more problems have been added to Practice 3. Their solutions have been added as well.

April 21

Isomorphisms. Matrices of linear transformations (6.3)

Read 6.2 and 6.3.

Suggested pb: page 387: 3, 5, 9, 13, 15, 17, 19, 29, 33, 35, 37, 47, 59.

April 23

Application of Linear Algebra

Link to $25,000,000 Eigenvector: the Linear Algebra behind Google is on Additional Resources page

April 28