Date  WORK DUE at the beginning of class or lab unless otherwise noted! 
16 Dec  Tues 
Comparison of Linear Algebra in the High School and University Setting: by Candace and Melissa Computer Programing with Matrices and Images: by Josh Computer Programming with Vectors: by Bethany Google's PageRank Algorithm: by Kaj Eigenvectors with Deer Populations and Hunters: by Alana Electronic Circuits: Isaac Fractals and Linear Algebra: Ondrej Java Program that Takes the Determinant of Matrices: Coty and Ryan Linear Algebra and Contra Dancing: by Katie Mebane Linear Algebra and Game Theory: Catherine Linear Algebra and Graphic Design: Darrell Linear Algebra and High School Math Education: by Caitlin and Katie Linear Algebra in Hydrogeology: by Anna Linear Algebra involved in Nash Equilibriums: by Jeremy and Justin Linear Algebra & Parimutuel Wagering Systems: by Stephen Linear Algebra and Sports Ranking: by Alex Linear Algebra and Temperature Distribution: Austin and Marc Matrices and Game Theory: by Amy and Philip Matrices and Fibonacci Numbers: by Becca Special Unitary Groups: by Davidson 
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9 Dec  Tues 

4 Dec  Thur 

2 Dec  Tues 

25 Nov  Tues 

20 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 explain 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. 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? 
18 Nov  Tuesday 

13 Nov  Thur 

11 Nov  Tuesday 

4 November  Tuesday 

30 October  Thursday 
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 Problems 2: 4.5 24 Problems 3: 4.5 48 Problem 4: Cement Mixing Continued (**ALL IN MAPLE**) This problem is worth more than the others Problems 5: 4.6 24 Problems 6: 4.6 27 
28 October  Tuesday 

23 October  Thursday 
4.4 11, 53 4.5 22 
21 October  Tuesday 
Note: You may work with two other people and turn in one per group. 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 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. 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. 
14 Oct  Tues 

9 Oct  Thur 
4.2 21 [Show that axiom 1 is violated, ie find two determinant 0 matrices that sum to a matrix with determinant nonzero] 
7 Oct  Tues 
4.1 35, 43, 52 
2 Oct  Thur 
4.1 7 and 49. 
30 Sep  Tues  
25 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=S^(1) b) Problem 7: 3.3 (50 parts a & c) 
23 Sep  Tues 
3.1 33 byhand using the cofactor expansion method. Expand along the first column to take advantage of the 0s, and then the 1st column of the next 4x4 matrix, and then the 3rd row of the 3x3 matrix. 3.2 25 byhand using some combination of row operations and the cofactor expansion method. 3.3 31 
18 Sep  Thur 
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%]. I have added a Stochastic/Markov System Demo in 2.5 (from class on 9/16) file so that you can review related content to help you. 
16 Sept  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 
11 Sep  Thu 
2.1 (byhand: 9, 32) 2.2 (byhand: 17, 18), (35 parts b and c) 
9 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 parts 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 
4 Sept  Thur 
1.2 25, 27, and (43 parts a) through d)  in parts b) and d) 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. 
2 Sept  Tues 
1.1 7, 15, 19, (59 parts b and c  if a part is false, provide a specific counterexample, if it is true, quote a phrase from the text), and 73. 
28 Aug  Thur 
