Homework Assignments
Advanced Linear Algebra, Math 499/599
Kriloff - Spring, 2008
Math 499 Math 599
Chapter 1 assignment due Tuesday, 1/22
1.2 #1, 4 - notice that the commutative, associative, and distributive axioms automatically hold in any subset S of a field.
1.3 #4, 7, 8 - solve #4 by hand and record your row operations using the notation e_r^c, e_{rs}^c, e_{rs} from class
1.4 #7, 9, 10 - use Maple for #7 and 9 (use the command with(linalg); to access the linear algebra commands)
1.5 #3, 6, 8
1.6 #2, 7, 8, 10

You may use Maple to help you with any problems except for 1.3 #4 which I'd like you to show me by hand.  Print any work done in Maple for at least 1.4 #7 and 9 and any others you would like to include.  (Please print double-sided and use the Zoom Factor option in the View menu and the Print Preview command to save paper.)

You are encouraged to redo #1.3.8, 1.4.10, 1.5.8, 1.6.7, 1.6.10 and optionally #1.3.7, 1.4.9, 1.5.6, 1.6.8 to turn in on Thursday, 1/31.
Do the 499 assignment plus 1.2 #7 and:
(A) Formulate a conjecture that generalizes the result in 1.5 #8 and prove at least the easy direction of your conjecture.
(B) Do you believe the result in 1.4 #10 is true for m x n matrices?  Why or why not?
Chapter 2 assignment due Tuesday, 2/5
2.1 #5
2.2 #1d,e, 2a,b, 8
2.3 #1, 7, 11
2.4 #4
2.6 #3, 4
Do the 499 assignment and:
2.2 #7
2.4 #6
3.1-3.3 assignment due Tuesday, 2/19
3.1 #1, 4, 5
3.2 #1, 3, 5
3.3 #2, 7
3.1-3.3 assignment due Tuesday, 2/19
3.1 #9, 12, 13
3.2 #3, 5, 8, 11
3.3 #2, 5, 7
3.4, 3.5, 3.7 assignment due Thursday, 3/13
3.4 #1 (show two ways to get the matrix for part (c)), 8, 10
3.5 #1, 2
3.7 #1, 5, 7

3.4, 3.5, 3.7 assignment due Thursday, 3/13
3.4 #6 (show two ways to get the matrix for part (b)), 8, 12
3.5 #15, 16
3.7 #5, 7, 8
6.2, 6.3 assignment due Thursday, 4/3
6.2 #5, 7, 10
6.3 #2, 3
6.2, 6.3 assignment due Thursday, 4/3
6.2 #7, 10, 15
6.3 #2, 9
6.4-6.8 assignment due Tuesday, 4/15
6.4 #1, 4
6.6 #1, 3
6.7 #2 (should reference 6.6 #1)
6.8 #1
6.4-6.8 assignment due Tuesday, 4/15
6.4 #4, 13
6.6 #1, 4
6.7 #2 (should reference 6.6 #1)
6.8 #1
Exam 3 Due Tuesday, April 29 (10 points each)
6.2 #4
6.3 #6
6.4 #9 (give a proof or counterexample in each case)
6.6 #5
6.8 #2
Exam 3 Due Tuesday, April 29 (10 points each except 6.6 #5 only 5 points and 6.7 #4 15 points)
6.3 #7
6.4 #9 (give a proof or counterexample in each case)
6.6 #5
6.7 #4 (note typo in part b - change f to T
6.8 #2