Math 320 - Linear Algebra I

Spring 2009

We meet at 10am - 10:50am, MWF, 220 Stevenson Hall (CRN 16474)

Contact info and Office hours:

Professor Brooke Shipley
Office: SEO 508
phone: (312) 996 6095
e-mail: bshipley@math.uic.edu
Office hours: Monday 2-3pm, Wednesday 3-4pm, Friday 11am-12pm

TA: Johnathon Schneider (jschne9@uic.edu)
REVIEW SESSION: Monday 3pm SEO 1227 (extra office hours Monday in MLC (SEO 4th floor) 4 - 6pm)

Book (See also syllabus here.):

We will be using the book by J. Hefferon "Linear algebra". The book and the solutions are available free on the website:
http://joshua.smcvt.edu/linearalgebra/
ftp://joshua.smcvt.edu/pub/hefferon/book/book.pdf
ftp://joshua.smcvt.edu/pub/hefferon/book/jhanswer.pdf

Grading:

Quizzes will be given about once a week (usually, but not always, announced beforehand). There will be two midterms.
Midterm I,II- 100pts each. Final - 200pts. Quizzes - 100pts. Total - 500pts.

Homework problems (For most problems solutions should be written down, but not turned in):

Week 1, January 12 - 16:

One.I.1, pp. 8-11, ## 1.16, 1.17, 1.19, 1.21, 1.22
One.I.2, pp. 18-20, ## 2.15, 2.16, 2.18, 2.23, 2.30
One.III.1, pp. 51-52, ## 1.7, 1.8, 1.9, 1.10

QUIZ on Friday Jan. 16

quiz.

Week 2, January 21 - 23:

2 problems TO TURN IN ("take home quiz") Wednesday January 21:

(at beginning of class, or *before* class in my mail box in SEO 302):
1. Find the solution set (in vector form, as in One.1.2) to the system of equations:
2x + 2y - 2z = 2
3x + 4y -6z = 5
x + 3y -7z = 5

2. Write down the sentence from the Syllabus that starts with "Copying."

Solutions to this "take home quiz."

Read the whole syllabus.

One.III.2, p. 59, # 2.11
One.I.2, pp. 18-20, ## 2.17, 2.20, 2.21

QUIZ on Friday Jan. 23

Solutions to this quiz.

Week 3, January 26 - January 30:

2 problems TO TURN IN ("take home quiz") Wednesday January 28:

(at beginning of class, or *before* class in my mail box in SEO 302):
1. Prove the following statement: Two matrices have the same reduced echelon form if and only if they are row equivalent. (Hint: This was proved quickly in class. Write down the complete argument using equivalence relation properties and quoting statements from the book.)
2. (This is written with row vectors, but should be with column vectors.) Is the vector (4 8 5) in the set of vectors given by (-1 1 -5 ) + (2 3 4) x + ( 1 1 2) y with x and y real numbers? (Hint: This can be rewritten as a linear system of equations. Then use Gauss-Jordan reduction to solve the system.)

Solutions to this take home quiz.

Two.I.1, pp. 88-91, ## 1.18(a,c), 1.19(a,c), 1.20(d), 1.21(a,c), 1.26(a), 1.40
Two.I.2, pp. 97-100, ## 2.20(a,d), 2.22(a,c), 2.24, 2.25(a,c), 2.26(a,d)

Class Quiz on Wednesday Jan. 28

class quiz.

Week 4, February 2 - 6:

2 problems TO TURN IN ("take home quiz") Wednesday, February 4:

(at beginning of class, or *before* class in my mail box in SEO 302):
1. Find a set (with at most five elements) which spans the space V = { a + bx + c x^2 such that a + c = 0 with a, b, c real numbers}. (The notation x^2 is read "x squared".)

2. Find a set (with at most five elements) which spans the space W' which is a subset of two-by-two matrices with entries:
(1,1) entry = a
(1,2) entry = b
(2,1) entry = c
(2,2) entry = a+b
such that b + c = 0 and a, b, c are real numbers.
Solutions to this take home quiz.

Brooke Shipley, SEO 508 (bshipley@math.uic.edu)
Office hours: Monday 2-3pm, Wednesday 3-4pm, Friday 11am-12pm

TA: Johnathon Schneider (jschne9@uic.edu)
REVIEW SESSION: Monday 3pm SEO 1227
(extra office hours Monday in MLC (SEO 4th floor, 436?) 4 - 6pm)

Two.II.1, pp. 108-111, ## 1.18(a,c), 1.19(b,d), 1.24, 1.28, 1.29
Two.III.1, pp. 116-118, ## 1.16(b,c), 1.17, 1.18, 1.19, 1.24(b,d), 1.28(a,c), 1.33
Two.III.2, pp. 122-123, ## 2.15, 2.18(b), 2.21, 2.22

There will be a quiz in class on Friday, February 6.

quiz.

3 problems TO TURN IN ("take home quiz") Monday, February 9:
(at beginning of class, or *before* class in my mail box in SEO 302):
1. Show that the set of 2 by 2 matrices forms a vector space.
2. Does the following set of vectors span R^3? (You can think of these as column vectors or row vectors.) {(1, 2, 3) , (1, 0, -1), (2, 2, 2), (2, 4, 6)}
3. (See 2.3.1.24) Find a basis in P_2 (polynomials of degree less than or equal to two) for the subspace of polynomials such that p(3) = 0.
Solutions to these problems.
Week 5, February 9 - 13:

There will be a quiz in class on Wednesday, February 11.

quiz.

On Wed. Feb. 11, Shipley's office hours will be 2-3pm (in SEO 508).
3 problems TO TURN IN ("take home quiz") Friday, February 13:
1. Prove that if {a, b, c} is a basis of V and w = a + 2b + 3c that V = Span{w, b, c}. (See the second part of the proof of 2.3.2.2.)

The next two problems are problems number 3 and 5 from this hard sample exam.
(Number 3: Define the rank of a matrix A and calculate the rank of A. See the pdf file for the 3 by 3 matrix with entries e^2, pi^2, 9; e, pi, 3; 2e, 2pi, 6.)
Number 5: Prove or disprove that real 2-space (R^2) with ordinary vector addition and scalar multiplication only on the first entry (see pdf file) is a vector space.
Solutions to these problems.

Two.III.3, pp. 129-130, ## 3.16(a,c), 3.17(a), 3.18(a), 3.20(b), 3.21(a,c), 3.28
Two.III.4, PP. 136-139, ## 4.20(a,d), 4.21, 4.23, 4.26, 4.34

Week 6, February 16 - 20:

Exam1 on Friday, February 20, 2009. (On Chapters One and Two.)

Hard Sample Exam (two sample exams handed out in class as well)>

Exam from Feb. 20, 2009

Solutions to Exam from Feb. 20, 2009

Week 7, February 23 - 27:

2 problems TO TURN IN ("take home quiz") Friday, February 27:

(at beginning of class, or *before* class in my mail box in SEO 302):
1. Refer to Three.I.1.16. Come up with two more isomorphisms between P_2 (polynomials of degree less than or equal to two) and R^3. Do not use the ones from Example 1.2 or the solutions to Three.I.1.16. Make sure for yourself that your maps are isomorphisms (but for this problem you don't have to show your work or justify these maps are isomorphisms.)
2. Produce an isomorphism between P_3 (polynomials of degree less than or equal to three) and the vector space of two by two real matrices (M_{2,2}). Show directly and in detail that your map is an isomorphism.
Solutions to these problems.

Three.I.1, pp. 160-162, ## 1.11, 1.13, 1.14, 1.19, 1.26
Three.I.2, pp. 168-169, ## 2.8, 2.12, 2.14
Three.II.1, pp. 175-177, ## 1.17(a,c), 1.18(b,c), 1.19
Three.II.2, pp. 186-188, ## 2.22, 2.23(a,b), 2.24(a,c)

Week 8, March 2 - 6:

There will be a quiz on Monday, March 2 (on isomorphisms and homomorphisms).
Solutions to the in class quiz.

Homework to turn in March 6: (on the long side, but you should have done most of these by February 27 anyway!)

Three.I.1, ## 1.13 (c,d), 1.19
Three.I.2, ## 2.8, 2.12
Three.II.1, ## 1.17(a,c), 1.18(b,c), 1.19(b)
Three.II.2, ## 2.22, 2.23(a,b), 2.24(a,c)
Three.III.1, ## 1.14, 1.15, 1.22, 1.26 (a,b)

Problems to look at for the lectures March 2-6.

Three.III.1, pp. 203 - ## 1.14, 1.15, 1.16, 1.22, 1.26
Three.III.2, pp. 209 - , ## 2.9(b,c), 2.10, 2.11, 2.13, 2.18

Week 9, March 9 - 13:

Problems to look at for the lectures March 9-13.

Three.IV.1,pp. 213- ## 1.7, 1.13, 1.14, 1.15
Three.IV.2, pp. 220-, ## 2.14, 2.16, 2.17
Three.IV.4, pp. 236-, ## 4.14, 4.16, 4.18, 4.19

In class quiz on Three.III on Wednesday, March 11:

Homework to turn in March 13:

Week 10, March 16 - 20:

Homework to turn in March 20 (or earlier!):

Problems to look at for the lectures March 16-18.

Three.V.1, pp. 241 , ## 1.6, 1.7(b,d), 1.8(b,d), 1.9(a,c), 1.10(b,c), 1.11
Three.V.2, pp. 247 ## 2.10, 2.12

Week 11, March 20, March 30 - April 3:

Problems to look at for the lectures March 20-April 3.

Four.I.1, pp. , ## 1.1(a,b), 1.4(c), 1.5(b), 1.7, 1.8
Four.I.2, pp. , ## 2.7(a,b), 2.9, 2.13, 2.16
Four.I.3, pp. , ## 3.27, 3.33
Four.Cramer's rule, p.331, ## 1,2

There will be a quiz on Friday, April 3.

Homework to turn in April 1 (or April 3, depending on when you want it graded and returned to you.) :

Week 12, April 6 - 10:

Midterm 2 on Chapter 3 and 4 (only sections listed above) on April 10.

OLD Topics and OLD Sample Exam

Two practice exams (on one sheet) were handed out in class on April 1. Here is a scan of (two copies of) the handout.

Here is a handout prepared by the grader to help distinguish between providing a counter-example and a proof.

This is the solution to the second midterm. If you print, print only pages 1 and 3; ignore pages 2 and 4.

Week 13, April 13 -17:

Five.II.3, pp ## 3.20(a,b,c,e), 3.21, 3.22, 3.23, 3.24(a), 3.28, 3.34, 3.37(a,b), 3.42

Five.II.1, pp ## 1.4, 1.6, 1.10, 1.11

Five.II.2, pp ## 2.7(a,b), 2.8, 2.9, 2.17

Homework to turn in April 17:

Five.II.3, pp. 364 ## 3.20(b,c), 3.21a, 3.23, 3.24(a), 3.37(a,b)

Five.II.1, pp. 354 ## 1.6, 1.11

Week 14, April 20 -24:

Three.VI.2, pp. , ##2.9(a,b), 2.10(a), 2.12, 2.16, 2.17, 2.19
Three. Orthonormal Matrices, pp. , ##1,2

Homework to turn in April 24:

Five.II.2, pp ## 2.7(a,b), 2.8, 2.9, 2.17

Three.VI.2, pp.258 , ##2.9, 2.10(a), 2.12, 2.16, 2.17(a,b)
Three. Orthonormal Matrices, pp. , ##1,2 (Careful, solutions to 2 (b,c) are incorrect.)

Announced QUIZZES: On Friday, April 24 and on Wednesday, April 29.
The last week of class will be review for the final.

Final Exam: 10:30-12:30 p.m., 220 SH (usual room), Friday, May 8, 2009!

This exam will cover material from the whole course. There will be a slight emphasis on the material covered since the second midterm.

This is a practice final exam. Another Sample Exam
Solutions to both practice exams are here. There is a mistake in the solutions for problem 3 on the 2006 exam. The first, second and fourth vectors listed are linearly independent. So dim S = 3 (not 2). The vectors k_1 and k_2 are correct, but there is a third vector k_3 as well. This also changes part (d).

Math 320 - Linear Algebra I

Spring 2009

Contact info and Office hours:

Book (See also syllabus here.):

Grading:

Homework problems (For most problems solutions should be written down, but not turned in):

QUIZ on Friday Jan. 16

2 problems TO TURN IN ("take home quiz") Wednesday January 21:

Read the whole syllabus.

QUIZ on Friday Jan. 23

2 problems TO TURN IN ("take home quiz") Wednesday January 28:

Class Quiz on Wednesday Jan. 28

2 problems TO TURN IN ("take home quiz") Wednesday, February 4:

There will be a quiz in class on Friday, February 6.

3 problems TO TURN IN ("take home quiz") Monday, February 9:

There will be a quiz in class on Wednesday, February 11.

3 problems TO TURN IN ("take home quiz") Friday, February 13:

Exam1 on Friday, February 20, 2009. (On Chapters One and Two.)

2 problems TO TURN IN ("take home quiz") Friday, February 27:

There will be a quiz on Monday, March 2 (on isomorphisms and homomorphisms).

Homework to turn in March 6: (on the long side, but you should have done most of these by February 27 anyway!)

Problems to look at for the lectures March 2-6.

Problems to look at for the lectures March 9-13.

In class quiz on Three.III on Wednesday, March 11:

Homework to turn in March 13:

Homework to turn in March 20 (or earlier!):

There will be a quiz on Friday, April 3.

Homework to turn in April 1 (or April 3, depending on when you want it graded and returned to you.) :

Midterm 2 on Chapter 3 and 4 (only sections listed above) on April 10.

Homework to turn in April 17:

Homework to turn in April 24:

Final Exam: 10:30-12:30 p.m., 220 SH (usual room), Friday, May 8, 2009!