Date  Work is always due at the BEGINNING of class 
12 Dec  Wed 

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6 Dec  Thur 

4 Dec  Tues 

29 Nov  Thur 

27 Nov  Tues 

20 Nov  Tues 
Note: You may work with two other people and turn in one per group of three Hints and Commands for Problem Set 6 
15 Nov  Thur 

13 Nov  Tues 

8 Nov  Thur 
Note: Since ASULearn is down, I linked recent ASULearn solutions for chapter 4 inside the study guide link. 
6 Nov  Tues 

1 Nov  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 and include the definition of span in your explanations Problem 2: 4.5 24 and include the definitions of basis, span and l.i. in your explanations Problem 3: 4.5 48 and include the definitions of basis, span and l.i. in your explanations 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 
30 Oct  Tues 
4.5 22 and Maple practice problem 
25 Oct  Thur 
4.4 11, 53 
23 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: True or False: The line x+y=0 is a vector space. (ie {(x,y) in R^2 so that x+y=0}, with addition and scalar multiplication of vectors in R^2 as usual) Problem 6: 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 of vectors in R^3 as usual). Problem 7: 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 (matrix addition as usual) of the set of nxn matrices. 
18 Oct  Thur 

16 Oct  Tues 
4.1 For #35, follow the instructions below: a) First solve this algebraically, by setting up the vectors as columns and reducing the augmented matrix for linear combinations. b) Then, as in Chapter 4, plot the columns of the coefficient matrix using commands like: with(plots): col1:=spacecurve([2*t,3*t,5*t],t=0..1): display(col1, col2, col3) Do the columns of the coefficient matrix lie in the same plane [ie can you turn to a "head on" view where they look like they are on the same line]? Explain. c) If your answer to b) was no then they will generate all of 3space under linear combinations, so anything will be a linear combination of them, so skip part c). However, if your answer to b) was yes, then add the Matrix([[10],[1],[4]]) vector into the spacecurve plot via col1:=spacecurve([10*t,1*t,4*t],t=0..1): display(col1, col2, col3, col4) to see if it also lies in that plane and describe. d) As in chapter 1, plot the three rows of the augmented matrix for the system using commands like row1:=implicitplot3d({2*x+y2*z10},x=20..20,y=20..20,z=20..20, color=yellow): display(row1,row2,row3) Are the rows lines or planes and how do they intersect [no common intersection, a single point, an entire line, or an entire plane]. Explain. 4.1 #43 4.2 # 21 [Show that axiom 1 is violated, ie find two determinant 0 matrices that sum to a matrix with determinant nonzero] 
9 Oct  Tues 
4.1 2, 4, 7 and 52. 
4 Oct  Thur 

2 Oct  Tues 

27 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 (50 parts a & c) 
25 Sep  Tues 

20 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 (IN)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%]. Reduce in Maple, but be sure to put in fractions instead of decimals. 
18 Sep  Tues 

13 Sep  Thur 
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 on Maple Problem 5: 2.3 14 by hand and on Maple Problem 6: 2.3 28 part a  write the matrix system as Ax=b and apply the inverse method of solution in Maple via MatrixInverse(A).b Problem 7: 2.3 40 part d 
11 Sep  Tues 
2.1 (byhand: 9, 32) 2.2 (byhand: 17, 18), (35 parts b and c) 
4 Sep  Tues 
Your explanations must distinguish your work as your own. Also give proper acknowledgment to any help. For true/false questions, if a part is false, provide a specific counterexample, if it is true, quote a phrase and page # from the text. Note: You may work with at most two other people and turn in one per group. Follow the directions below. If it does not specify you may use any combination of Maple and byhand that you like, but no calculators since you must print or show all your work. Problem 1: 1.1 60 part c Problem 2: 1.1 74 using GaussianElimination(N) in Maple and then reason from there Problem 3: 1.2 30 by hand and on Maple using ReducedRowEchelonForm(M) Problem 4: 1.2 32 on Maple using ReducedRowEchelonForm(M) 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 
30 Aug  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. 
28 Aug  Tues 
1.1 55, (59 parts b and c), and (73 use byhand Gaussian to obtain 0s below the diagonal, with operations like r3'=k*r1+r3, and then reason from there using the last row of the Gaussian eliminated matrix). 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. For true/false questions, if a part is false, provide a specific counterexample, if it is true, quote a phrase and page # from the text. 
23 Aug  Thur 
1.1 7, 15, 19 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. 