Numerical Linear Algebra

Date Assigned 
Section 
Page 
Problems 

23 Aug  send email to me  
28 Aug  1.1  10  # 3, 7, 14, 18, 27, 31, 33 
28 Aug  1.2  25  # 2, 6, 11, 16, 21, 23, 26, 27 
28 Aug  1.3  36  # 5, 11, 14, 17, 19, 22, 25 
30 Aug  1.4  46  # 3, 4, 7, 10, 12, 22, 25, 31 
4 Sep  1.5  54  # 5, 8, 13, 16, 21, 23, 2932, 37 
4 Sep  1.6  64  # 713, 19, 22, 23, 27, 29, 38a 
6 Sep  1.7  73  # 3, 8, 9, 11, 36, 38 
11 Sep  1.8  83  # 1, 4, 7, 17, 18, 26, 28, 29 
13 Sep  1.9  93  # 5, 7, 8 
18 Sep  2.1  107  # 2, 3, 6, 8, 9, 12, 15 
18 Sep  2.2  117  # 3, 6, 7a, 9, 10, 17, 29, 32, 35, 37 
18 Sep  2.3  123  # 1, 46, 1624 
25 Sep  Exam 1  Chapter 1 and Sections 2.12.3  
27 Sep  2.4  130  # 2, 4, 5, 8, 22 
2 Oct  2.5  139  # 1, 6, 9, 15, 16, 26 
4 Oct  2.6  147  # 1, 4, 5, 8, 12, 17 
9 Oct  2.7  153  # 14, 5, 7, 1315 
11 Oct  2.8  163  # 2, 4, 5, 8, 9, 11 
18 Oct  4.1  217  # 1, 4, 5, 8, 12, 17 
23 Oct  4.2  228  # 3, 5, 11, 16, 22, 23, 38 
25 Oct  4.3  237  # 1, 2, 3, 5, 6, 14, 16, 17 
30 Oct  4.5  255  # 1, 6, 7, 9, 11, 14, 17 
30 Oct  4.6  263  # 3, 6, 7, 11, 13, 15, 19, 20 
1 Nov  4.4  248  # 2, 6, 9, 13 
1 Nov  4.9  290  # 1, 4, 8, 9, 14, 21 
6 Nov  Exam 2  Chapters 2 and 4  
8 Nov  5.1  302  # 1, 8, 10, 15, 17, 21 
13 Nov  5.2  311  # 2, 3, 17, 21 
13 Nov  5.3  319  # 1, 6, 9, 14, 23, 24 
15 Nov  5.8  363  # 1, 7, 11, 19 
15 Nov  6.1  376  # 1, 4, 5, 10, 20, 27 
20 Nov  6.2  386  # 2, 7, 13, 24, 29 
27 Nov  6.3  395  # 1, 7, 13 
29 Nov  6.4  402  # 2, 13, 17 
29 Nov  6.5  411  # 3, 6, 7, 12, 17, 19, 22 
4 Dec  6.6  420  # 2, 8, 11 
4 Dec  7.1  448  # 3, 4, 6, 10, 11, 15, 20, 25 
13 Nov  Final Exam  9:00amnoon  Comprehensive 
Date Due  Points  Assignment 
27 Nov  10  MATLAB can be used for some rather incredible things. For example,
several pictures can be encoded in a single MATLAB image with a clever
use of floating point numbers. Execute the following MATLAB statements:
id = get(image,'CData'); id = (idfloor(id))*32; image(id);Repeat the last two commands several times. Provide a complete list of all the different images you see. Explain what is being done in the reassignment of id. What is the maximum number of images that could be stored in this manner? 
27 Nov  10  Prove: Halloween = Christmas.
Hint: Write the dates like I do and think about other (number) bases. 
Date Assigned 
Date Due 
Title 
Text Reference 
Comments 

29 Aug  4 Sep  Getting Started with MATLAB  good introduction to MATLAB geared towards the needs of this course  
29 Aug  4 Sep  Practice Row Operations  Section 1.2  provides practice obtaining an echelon form of a matrix with row operations using the replace, swap, and scale commands 
5 Sep  10 Sep  Exchange Economy and Homogeneous Systems  Section 1.5  Find equilibrium prices for an exchange economy 
5 Sep  10 Sep  Population Migration  Section 1.9 (Exercise 11)  More detailed, and interesting, version of Exercise 11 in Section 1.9 of the text 
12 Sep  17 Sep  Visualizing Linear Transformations of the Plane  Sections 1.7 and 1.8  To understand the standard matrix of a linear transformation, particularly for shears, rotations, reflections, contractions, and extensions. 
19 Sep  25 Sep  Rank and Linear Independence  Section 1.6  To define the rank of a matrix and to learn its connection with linear independence of the columns of a matrix. 
26 Sep  2 Oct  Using Backslash to Solve Ax=b  Section 2.2  To learn about MATLAB's backslash command (\) and why it is preferred over explicit computation of a matrix inverse or Gaussian elimination for solving systems Ax=b when A is invertible. 
26 Sep  2 Oct  Roundoff Error in Matrix Calculations  Section 2.2  Continues the investigation of the previous lab with an emphasis on floating point computations, including an introduction to the condition number of a matrix. 
3 Oct  9 Oct  Schur Complements  Section 2.4  To learn about Schur Complements and their connection with row reduction. 
10 Oct  17 Oct  LU Factorization  Section 2.5  To practice the LU factorization algorithm discussed in the text and to compare this with the results of MATLAB's lu command. 
17 Oct  23 Oct  An Economy with an Open Sector  Section 2.7  More investigation of Leontief Input/Output Models. 
17 Oct  23 Oct  Matrix Inverses and Infinite Series  Section 2.7  To see examples when the inverse of (IC) can be obtained as an infinite series I + C + C^2 + ... and when this infinite series does not converge to the inverse. 
23 Oct  29 Oct  Partitioned Matrices  Section 2.4  To obtain more experience and familiarity working with partitioned matrices. 
30 Oct  6 Nov  Subspaces  Section 4.1  To obtain a more complete understanding of span, basis, and dimension. In particular, to realized that subspaces with the same dimension are not necessarily equal. This project is good practice for Exam 2. 
7 Nov  13 Nov  Markov Chains and LongRange Predictions  Sections 2.1 and 4.9  To investigate several Markov chains and to investigate the longterm properties of these problems. 
14 Nov  20 Nov  Real and Complex Eigenvalues  Sections 5.1 and 5.5  To learn how to use MATLAB to find eigenvalues, including complexvalued eigenvalues (and eigenvectors). 
28 Nov  4 Dec  Using Eigenvalues to Study Spotted Owls  Sections 5.1, 5.5, and 5.6  To use eigenvalues to identify the critical juvenile survival rate that guarantees the the longterm success of the spotted owl population. 
5 Dec  11 Dec  Least Squares Solutions and Curve Fitting  Section 6.6  To obtain numerical and graphical experience using least squares to fit experimental data. 
Date Created 
Filename 
Comments 

6 Sep  Exercises from Sections 1.6 and 1.7  
11 Sep  Examples for Sections 1.8  
13 Sep  Solution to Quiz 3 and Example for Section 1.9  
4 Oct  Example of Jacobi and GaussSeidel iterative methods and the importance of diagonal dominance (Section 2.6)  
9 Oct  Leontief InputOutput Model Examples (Section 2.7)  
11 Oct  Applications to Computer Graphics (Section 2.8)
Auxiliary files: [ 

23 Oct  Example with Nul A and Col A (Section 4.2)  
25 Oct  Examples with bases, column spaces, and null spaces (Section 4.3)  
30 Oct  Examples with bases, column spaces, and null spaces (Section 4.3)  
1 Nov  Applications to Markov Chains (Section 4.9)  
1 Nov  Solution to Quiz 9  
15 Nov  Iterative Estimates for Eigenvalues (Section 5.8)  
15 Nov  Orthogonal Matrices and Projections (Sections 6.2 and 6.3)  
27 Nov  Solution to Extra Credit #1  
29 Nov  Examples with the GramSchmidt Process and the QR Factorization (Section 6.4)  
4 Dec  Examples with Linear Models (Section 6.6)  
6 Dec  Examples of Orthogonal Diagonalization (Section 7.1) 
Notes: