Math 324 Linear Algebra II

Monday, Wednesday, and Friday 9:10-10:00am

Hayes Hall 203

Textbook

Linear Algebra, A Modern Introduction, Third Edition, by David Poole.

Syllabus

Office Hours (Hayes 309-A)

Monday 2:10-3:00pm

Tuesday 11:10am-1:00pm

Wednesday 2:10-3:00pm

Thursday 10:10-11:00am

Homework

 Lesson Date Section(s) Topic Homework Due 1 1/14/2013 6.1 Vector Spaces and Subspaces Worksheet: #3 #10: Give a rigorous argument that each of the 10 properties holds for the vector space. Read Syllabus and Section 6.1. 1/16/2013 2 1/16/2013 6.1 Vector Spaces and Subspaces Worksheet: #6, 7, 9d In questions 6 and 7, just give a yes/no answer for (a). Also for 6 and 7, provide a spanning set for  that is as small as possible. Section 6.1: #4, 17, 18 (just show that axioms 1 and 6 hold), 22, 23, 38, 53, 55-57, 63, 64 1/23/2013 1/18/2013         1/21/2013 6.2         6.2 Linear Independence, Basis, and Dimension Section 6.2: #3, 7, 13, 21, 22, 23, 27, 28, 34, 36, 39, 48, 49 Section 6.2 Worksheet (not Wronskian worksheet): #5 Think about #6, 7 for Wednesday. Read Section 6.2. 3 1/23/2013 6.3 Change of Basis Section 6.3: #2, 6, 10, 13, 16, 20, 21 Section 6.2: #33 (write up both halves) The Shape of the Future, Back to the Future Worksheets Read Section 6.3, 6.4, and 6.5. 1/30/2013 4 1/30/2013, 2/1/2013, 2/4/2013, 2/6/2013 6.4-6.5 Linear Transformations, Kernel, Range, Isomorphism Sec 6.4: #5, 16, 20, 24, 30, 34, Sec 6.5: #4, 8, 14, 21, 26, 32, 33, 37 Read Section 6.6, prepare presentations. 2/6/2013 5 2/8/2013, 2/11/2013 6.6 The Matrix of a Linear Transformation Worksheet Sec 6.6: #15, 29, 39, 45, 46 Challenge Problems (read as “fun but not required”): 40, 41 2/13/2013 6 2/13/2013, 2/15/2013 Chapter 6 Review Review worksheet (to be graded for completion) Read Section 7.1. 2/20/2013 7 2/20/2013, 2/22/2013 7.1 Inner Product Spaces Sec 7.1: #2, 4, 9-11, 13, 16, 18, 20, 21, 27, 32 7.0 Taxicab: #6-8 Worksheet on Read Section 7.2. Challenge Problem: Prove that projW(v) and perpW(v) are orthogonal. 2/27/2013 8 2/25/2013, 2/27/2013, 3/1/2013, 3/18/2013 7.2 Norms and Distance Functions Sec 7.2: #2-4, 7-9, 14, 15, 24, 30, 32, 33, 40, 43, 45, 46, 48 Read Sections 7.3 and 7.4. 3/20/2013 9 3/22/2013, 3/25/2013 7.3 Least Squares Approximation HW from Jacobi proof: . Sec 7.3: #10, 16, 24, 26, 29, 34, 28, 38, 44, 50, 53-55 3/27/2013 10 3/25/2013, 3/27/2013 7.4 The Singular Value Decomposition! :) Section 7.4: #11, 15, 18, 19, 21, 24-30, 34, 35 #65: For the matrix A in question 10, confirm that each part of Theorem 7.15 holds. Challenge Problems: (1) Prove Thm 7.15(a) by proving Section 3.5 #61. (2) Prove Thm 5.25 and explain its connection to the svd. You may use a computer algebra system to help with computations for this assignment (such as computing eigenvectors of ATA), but you should make a note to that effect and write what the output at each step is. 4/3/2013 11 3/29/2013, 4/1/2013, 4/3/2013, 4/5/2013 7.4, Matlab The Singular Value Decomposition In-class worksheet MatLab Problems (Choose 2 from the list of 5) Email Professor Smith with questions if you haven’t done so yet! 4/10/2013 12 4/8/2013, 4/10/2013, 4/12/2013 7.4 The Singular Value Decomposition Section 7.4: #39, 40, 43, 47, 51 4/17/2013 13 4/17/2013 Chapter 7 Review Review assignment – not to be collected. Chapter Review, pg. 646-647: 1 (b)-(d), (h)-(j), 2-6, 7 or 8, 9-11, 13, 15-17, 19 (Show (PAQ)T(PAQ) is similar to ATA – why is this sufficient?) 4/22/2013, Saturn, Classifying Pictures Exciting applications! Work on project 1! 4/24/2013 4/24/2013, 4/26/2013 Cats and Dogs Again! Work on project 2! 4/29/2013