Date  WORK DUE at the beginning of class or lab unless otherwise noted! 
25 June  Fri 
Travis Baxter: Crystals Jenna Cantrell: Prisoner's dilemma and Nash equilibrium Thomas Capranica: NFL Quarterback Rating Colin Curtis: Pseudoinverse Cole Ditchman and Bradley Sheets: Matrix Encryption and Decryption Jacob Edwards: The Eight Queens Problem Clinton Freeman: Linear Algebra applications to computer graphics, such as collision detection, rotations, etc. Nick Galloway: Forest Management Bobby Lunceford: HITS (hyperlinkinduced topic search) algorithm Lauren Elizabeth Mitchell: NFL quarterback rating system 
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24 June  Thur 

23 June  Wed 

24 June  Tues 

21 June  Mon 
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? 
18 June  Fri 

17 June  Thur 

16 June  Wed 

15 June  Tues 
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 
14 June  Mon 

11 June  Fri 
4.4 11, 53 4.5 22 
10 June  Thur 
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). 
9 June  Wed 
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 June  Tues 
4.1 7 and 49. 
7 June  Mon 

4 June  Fri 

3 June  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) 
2 June  Wed 
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%]. 
1 June  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 
30 June  Mon 
2.1 (byhand: 9, 32) 2.2 (byhand: 17, 18), (35 parts b and c) 
28 May  Fri 
Note: You may work with at most two other people and turn in one per group but each person must complete and turn in Problem 3 themselves (in their own words). 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 
27 May  Thur 
1.2 25, 27, and (43  in addition to the directions in the book, 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. 
26 May  Wed 
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. 