Date  WORK DUE at the beginning of class or lab unless otherwise noted! 
11 Dec  Fri 

3 Dec  Thur 
Bioinformatics and Linear Algebra: Amanda Jones Conway's Game of Life: Joe Cramer's Rule: Ashley Carrigan Cryptography: Yeoly Ly Cryptography and Matrices: Katie Farmer and Meagen McAndrews Diagonalization of inertial tensors to find the principle axes: Kevin Holway and Luke Eight Queens and Determinants: Robert Bost and Kelly Eigenfaces and Facial Recognition: Jeremy Coleman Hill Ciphers and Linear Algebra: Cayley Strub Images in Java: Shawn Lights Out: Brett Coleman Linear Algebra in High School: Megan Ames Linear Algebra in High School: Josh Prince Thermal Profiles of an Urbanized Stream and Matrices: Rachel Networks: Tim Gallagher Rubik's Cube and Matrices: Ryan Belt Shear Matrix Applications: Katie Owens and Miranda Neaves 
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1 Dec  Tues 

23 Nov  Tues 

19 Nov  Thur 
Note: You may work with two other people and turn in one per group of three Hints and Commands for Problem Set 6 Problem 1: 7.1 #14 by hand and on Maple via the Eigenvectors(A); command also compare your answers and resolve any apparent conflicts or differences. Problem 2: Rotation matrices in R^{2} Recall that the general rotation matrix which rotates vectors in the counterclockwise direction by angle theta is given by M:=Matrix([[cos(theta),sin(theta)],[sin(theta),cos(theta)]]); Part A: Apply the Eigenvalues(M); command. Notice that there are real eigenvalues for certain values of theta only. What are these values of theta and what eigenvalues do they produce? (Recall that I = the square root of negative one does not exist as a real number and that cos(theta) is less than or equal to 1 always.) Part B: Find a basis for the corresponding eigenspaces. Part C: Use only a geometric explanation to explain why most rotation matrices have no eigenvalues or eigenvectors (ie scaling along the same line through the origin). Problem 3: 7.2 7 Problem 4: 7.2 18 Problem 5: 7.2 24 Problem 6: Foxes and Rabbits (Predatorprey model) Suppose a system of foxes and rabbits is given as: Part A: Write out the Eigenvector decomposition of the iterate x_{k}, where the foxes F_{k} are the first component of this state vector, and the rabbits R_{k} the second. Part B: Use the decomposition to explore what will happen to the vector x_{k} in the longterm, and what kind of vector(s) it will travel along to achieve that longterm behavior, and then fill in the blanks: If ___ equals 0 then we die off along the line____ [corresponding to the eigenvector____], and otherwise we [choose one: die off or grow or hit and then stayed fixed] along the line____ [corresponding to the the eigenvector____]. Part C: Determine a value to replace 1.05 in the original system that leads to constant levels of the fox and rabbit populations (ie an eigenvalue of 1), so that eventually neither population is changing. What is the ratio of the sizes of the populations in this case? 
12 Nov  Thur 

10 Nov  Tues 
1) Skim 7.1 to find the definition for an eigenvalue and an eigenvector and write it down. 2) Research the web for information about eigenvectors and write down a few items that you found interesting. 
5 Nov  Thur 

3 Nov  Tues 

29 Oct  Thur 
Note: You may work with two other people and turn in one per group. Hints and Commands for PS 5 Problem 1: 4.4 16 Problem 2: 4.5 24 Problem 3: 4.5 48 Problem 4: Cement Mixing Continued (**ALL IN MAPLE**) This problem is worth more than the others Problem 5: 4.6 24 Problem 6: 4.6 27 
27 Oct  Tues 

22 Oct  Thur 
4.4 11, 53 4.5 22 
20 Oct  Tues 
Hints and Commands for Problem Set 4 Problems 1: 4.1 36 Problem 2: 4.1 44 Problem 3: Cement Mixing (*ALL IN MAPLE*) *This problem is worth more than the others. Problem 4: 4.2 22 Problem 5: Natural Numbers Prove that the natural numbers (scalar multiplication as usual) is not a vector space using axiom 6. Problem 6: True or False: The line x+y=0 is a vector space. Problem 7: Solutions to the plane 2x3y+4z=5, ie {(x,y,z) in R^3 so that 2x3y+4z=5} Prove that this is not a subspace of R^{3} using axiom 1 (addition as usual). Problem 8: 4.3 (14 part D  Be sure to leave n as general as in class  do not define it as 2x2 matrix). Prove that this is not a subspace (addition as usual). 
13 Oct  Tues 
4.1 35, 43, 52 4.2 21 [Show that axiom 1 is violated, ie find two determinant 0 matrices that sum to a matrix with determinant nonzero] 
8 Oct  Thur 
4.1 7 and 49. 
1 Oct Thur  
29 Sep Tues  
24 Sep  Thur 
Note: You may work with at most two other people and turn in one per group. Maple Commands and Hints for PS 3 I also encourage you to ask me questions about anything you don't understand in office hours or message me on ASULearn. Your group's explanations must distinguish your work as your own. Problem 1: 2.5 24 Problem 2: Healthy/Sick Workers (all on Maple including text comments) *This problem is worth more than the others. Problem 3: 3.1 47 part a Problem 4: 3.2 32 part c Problem 5: 3.3 (28 byhand and on Maple) Problem 6: 3.3 (34 if a unique solution to Sx=b exists, find it by using the method x=MatrixInverse(S).b in Maple). Problem 7: 3.3 (50 parts a & c) 
22 Sep  Tues 
Part A Set up the stochastic matrix N for the system. The first column of N represents A>A, A>B, and A>Neither [.75, .20, .05 is the first column; .75, .15, .10 is the first row]. Part B Using regularity, we can see that the system will stabilize since the columns add to 1, and the entries are all positive. Find the steadystate vector by setting up and solving (NI)x=0 for x. Recall that if you add a row of 1s at the bottom, this will solve for the value you want [the entries add to 100%]. 
15 Sep  Tues 
Note: You may work with at most two other people and turn in one per group. Maple Commands and Hints for PS 2 I also encourage you to ask me questions about anything you don't understand in office hours or message me on ASULearn. Your group's explanations must distinguish your work as your own. Problem 1: 2.1 30 Problem 2: 2.2 34 parts a, b & c Problem 3: Show that the following statements about matrices are false by producing counterexamples and showing work: Statement a) A^{2}=0 implies that A = 0 Statement b) A^{2}=I implies that A=I or A=I Statement c) A^{2} has entries that are all greater than or equal to 0. Problem 4: 2.3 12 Problem 5: 2.3 14 by hand and on Maple Problem 6: 2.3 28 part a  look at the matrix system as Ax=b and then apply the inverse method of solution Problem 7: 2.3 40 part d 
10 Sep  Thur 
2.1 (byhand: 9, 32) 2.2 (byhand: 17, 18), (35 parts b and c) 
8 Sept  Tues 
Note: You may work with at most two other people and turn in one per group. Problem Set 1 Maple Commands and Hints. I also encourage you to ask me questions about anything you don't understand in office hours or message me on ASULearn. Your group's explanations must distinguish your work as your own. Problem 1: 1.1 60 part c Problem 2: 1.1 74 Problem 3: 1.2 30 by hand and also on Maple Problem 4: 1.2 32 Problem 5: 1.2 44 parts a) through d)  in b) and d) find all the values of k and justify Problem 6: 1.3 24 parts a and b Problem 7: 1.3 26 
3 Sept  Thur 
1.2 25, 27, and (43  find all the values of k and justify why these are all of them). Do not worry about getting the same answer as the back of the book (although it would be nice!) but do concentrate instead on making sure you understand the method of Gaussian Elimination. 
1 Sept  Tues 
1.1 7, 15, 19, (59 parts b and c), and 73. Don't worry about getting the correct answer  instead concentrate on the ideas and the methods. This will count as participation and will not receive a specific grade, although I will mark whether you attemped the problems. For true/false questions, if a part is false, provide a specific counterexample, if it is true, quote a phrase from the text. 
27 Aug  Thur 
