Math 307 Matrices and Linear Algebra Fall 2007

         New Information

Problem discussion (review problems below) Monday December 10 1-2 PM in 268 Carver.

Final Exam Information:

Approximatately 1/3 of the final will be on material after Test 3 (Sections 8.1-8.4 and 7.2).  The rest will be comprehensive.  Note:
1) Much of Ch 1 is subsumed in the rest of the course and thus does not need to be tested directly.
2) You can expect a question of the form "show W is a subspace of V or give an example to show it is not." 

Review problems:
1.2.7f, 1.3.1ac, 1.3.14ac, 1.4.36, 1.5.24bf, 1.6.1d, 1.8.1ace, 1.8.7h, 1.8.22a, 1.9.1f,
2.2.2ac, 2.2.12cg, 2.2.15de, 2.33.3bc, 2.3.7a, 2.3.8bc, 2.3.17, 2.3.21bd, 2.3.26, 2.3.33ab,
2.4.3b, 2.4.8b, 2.4.9b, 2.5.1cd(bases), 2.5.9, 2.5.21c,
3.2.2a, 3.2..4c, 3.2.22, 3.2.31, 3.3.2b, 3.3.32ab, 3.4.1ce, 3.4.22a(iii)
5.2.1b, 5.2.6a, 5.3.10, 5.3.27c, 5.5.5a, 5.5.11b
7.1.2ac, 7.1.15df, 7.2.24b, 7.2.25b, LH5,
8.2.1ce, 8.2.21, 8.2.32bc, 8.3.3ae, 8.3.15ae, 8.4.1bd

All graded work (except the final) has been completed.  I suggest you check all your scores (in WebCT).

Index

Homework Assignments

Always read the section of the text on which problems are assigned.
The problems are due on the Wednesday after they are assigned and will accepted through 9 AM the Friday following the week in which they are assigned (Aug. 20-Aug. 24 will be accepted through 9 AM Aug. 31).   When handed in, homework assignments should be stapled into one packet, in order.

date section problems
M 20-Aug 1.1, 1.2
 1.1.1(a)(b); 1.2.1, 1.2.5(a), 1.2.7, 1.2.13
W 22-Aug
 1.3
 1(a)(d), 2(b), 7, 9(a), 14, 15, 18(a), 19(a)(d), 32(b)
F 24-Aug
 1.4
 2(a)(b)(c), 3(a), 6, 9, 13
M 27 Aug
 1.4, 1.5
 1.4.19(a)(b)(d), 1.4.24;  1.5.1(a), 1.5.3(a)(b)(c)(d), 1.5.4, 1.5.8
W 29 Aug
 1.5
 24(a)(b)(d)(e), 25(a)(e), 28
F 31 Aug
 1.6
 1, 3, 5, 6 17, 19, 24
W Sept 5
 1.8
 1(a-d), 2(a-d), 4, 5, 7(a-g), 9, 10, 12, 13, 14, LH1
F Sept 7
 1.9
 1(a-f), 3, 5, 6, 7, 8
M Sept 10
 2.1
 1, 7, LH2
M Sept 17
 2.2
 1, 2abci, 4, 5, 12, 15
W Sept 19
 2.3
 1,3,4,6,7,8
F Sept 21
 2.3, 2.4
 2.3.21, 2.3.25, 2.3.26, 2.3.27;  2.4.1, 2.4.2
M Sept 24
 2.4
 4, 8, 9, 10
W Sept 26
 2.5
 1(find basis for ker and rng), 5a-d, 21, 22i,ii, 25a-d
F Sept 28
 3.1
 2,3,4a
M Oct 1
 3.2
 1ab, 2a, 5, 15, 16, 32ab
W Oct 3
 3.3
1, 2(norms only)ac, 20, 23, 31, 32, 35
F Oct 5
 3.4
 1,2,3,4, LH3
M Oct 8
 3.6
 review for Test 2
M Oct 15
 5.1
 1, 8, 18, 21
W Oct 17
 5.2
 1ab, 3, 4bc, 6, 9c
F Oct 19
 5.3
M Oct 22
 5.3
 1, 3, 6, 7, 10, 14, 26, 28
W Oct 24
 5.5
 2, 3, 4
F Oct 26
 5.5
 10, 11, 12, 13, 27 (any valid method ok for these problems)
M Oct 29
 5.7
 1bc
W Oct 31
 7.1
 1, 2, 6, 7, 9
F Nov 2
 7.1
 5abcd, 19a-g, l, p, 27ab, 37ab, 38, 51a-d
M Nov 5
 7.1
M Nov 12
 7.2
 24, 25, LH5
W Nov 14
 7.2, 8.1
 7.2.26abc, 8.1.1, 8.1.2, 8.1.3
F Nov 16
 8.2
 1 (not g or other complex eigenvalues)
M Nov 26
 8.2
 14, 20-22
W Nov 28
 8.3
 1abcdeh, 2abeh, 15a-f, 19abc
F Nov 30
 8.4
 1abc, 2 (eigenvalue method only)

LH1: Determine which of the following matrices are row equivalent to each other:
       (-2  5   6)            (  0 -2  0)             (  0 -2  0)
A=  ( 1  1 -3)      B = (-2 -2 -6)      C = (-2 -2   6)        
       (-3  3   9)            (  1  0   3)            ( 2  2  -6)

LH2: Compute det B and det C if det A = -5, where
       (a b c)             (  a    d     g )             (a-d b-e c-f)
A=  (d e f)      B = ( 2c   2f   2i )      C = (d-g e-h f-i)        
       (g h i)             (b+c e+f h+i)             (g-a h-b i-c)

LH3: (a) Compute the Gram matrix G=G_<,>(v,w,u) and (b) find nonzero z such that Gz=0 where
<x,y>=3 x1 y1 + 2 x2 y1 + 2 x1 y2 + 5 x2 y2 and
v = (1,1)^T, w=(1,-1)^T, u=(1,2)^T.

LH4: Show that L is a linear transformation or give an example to show it is not.
a) L:2 x 2 matrices to 2 x 2 matrices by L(A)=A^T (transpose of A)
b) L:2 x 2 matrices to R by L(A)=det A

LH5:  For the given ordered basis B=(b_1,....b_n) of vector space V and vector v in V,
find the coordinate vector of v with respect to B, i.e. [v]_B.
a) V = P_3, B=(b_1=1, b_2=x, b_3=x^2, b_3=x^3, b_4=x^3), v=3x^3-5x+2
b) V=R^2, B=(b_1=[1,-3]^T, b_2=[1,-2]^T), v=[1,1]^T
c) V=R^3, B=(b_1=[1,1,1]^T, b_2=[1,-2,-1]^T), v=[3,-1,0]^T), v=[1,2,3]^T

Computations for modified Ex 5.62

Test Information

Test 1 is Friday, Sept. 14 and will cover material from the text and presented in class related to Chapter 1 (excluding 1.7).
It will not cover Section 2.1. Calculators are not necessary and not permitted.  The homework provides good preparation for the test.  There will be a review in class Wed. Sept. 12.

Test 1 solutions   Test 1

Test 2 is on Friday Oct. 12 and will cover Chapter 2 (2.1-2.5) and Chapter 3 (3.1-3.4).
One question will be (for some specific W subset of vector space V):
Either show the set W is a subspace of V or give an example to show that W is not a subspace of V.
To prepare for this question, the following problems are recommended:
2.2: 2, 7, 9, 10, 11, 12, 13a-g, 14, 15a-f.
The review on Wednesday Oct. 12 will briefly list the topics covered on the test, and then most of the time will be spent discussing questions.

Test 2 partial solution

Test 3 will cover Sections 5.1, 5.2, 5.3, 5.5, and 7.1 (pp. 331-336)
Review problems (for discussion Wednesday Nov. 7):
5.2: 1,3,4,6,9
5.3: 1,10,26,28
5.5: 2,3,4,5,10,12,13,27, 11
7.1: 1,2, LH4

Class Time and Place

        MWF 9-9:50 in 74 Carver

Text

Applied Linear Algebra by Olver & Shakiban

Course Content

See Calendar for sections to be covered

Polices/Syllabus

Instructor Information

Disability Information Iowa State University complies with the American with Disabilities Act and Section 504 of the Rehabilitation Act.  If a student has a disability that qualifies and requires accommodations, he/she should contact the Disability Resources (DR) office for information on appropriate policies and procedures. DR is located on the main floor of the Student Services Building, Room 1076; their phone is 515-294-6624. Any student who requires an accommodation under such provisions should contact me privately as soon as possible and no later than the end of the first week of class or as soon as documentation of the need for accommodation is obtained. Contact may be made by e-mail (LHogben@iastate.edu), telephone (4-8168), or in person (office 488 Carver).  No retroactive accommodations will be provided in this class.
 
 
 
 
Leslie Hogben's Homepage updated after each class period