Math 405 (Laskowski) Homework, Spring, 2016
There will be at least 11 homework assignments worth 20 points each. These are
given below, but are subject to changes announced in class. Only your
10 best homework scores count toward your course grade.
Homeworks are due at the beginning of class (i.e., 12:30pm) on the dates indicated below.
If the University cancels class for any reason on the scheduled
due date of an assignment then that assignment will be due on the
first day that the class subsequently meets. Assignments turned
in late will be recorded, but may not be graded for full credit.
How Each Homework Should Look. Your homework should be neat
and legible. You should give the number of each problem attempted and
the work for each problem should be indicated clearly. (There should
be no arrows running around or between pages!) The reasoning behind
each answer should be given. Your answers should be presented in the
order that the problems are assigned. If you use more than one sheet
of paper, they should be stapled together. The top of the first page
should include: your name, our course and section number, my name, and
the date the assignment is due.
How Each Homework Will Be Graded. Your score for each
homework assignment will be the sum of your scores of the problems
renormalized so that the maximum possible score on each assignment
is 20 points.
Homework Assignments
-
Tuesday, February 9 (Vector spaces and subspaces)
- Curtis, Section 3: 1.
- Curtis, Section 4: 1, 3, 4, 6, 7, 8.
-
Tuesday, February 16 (Bases, dimension, and elementary row operations)
- Curtis, Section 5, page 37 # 3, 4, 5
- Curtis, Section 6, page 48 # 1, 2, 5
- Curtis, Section 7, page 52 # 1, 3, 4, 6.
-
Tuesday, February 23 (Systems of linear equations and linear manifolds)
- Curtis, Section 8, page 61 # 1a,b,e, 3.
- Curtis, Section 9, page 68 # 2a,b,e, 3.
- Curtis, Section 10, pp 73-74 # 1b, 3, 4, 7.
-
Tuesday, March 1 (Linear transformations)
- Curtis, Section 11, pp 87-88 # 3, 4, 6a,b, 8a,b, 10.
- Curtis, Section 12, pp 98-99, # 3c, 7a,b,c, 8.
-
Tuesday, March 8 (Linear transformations and inner products)
- Curtis, Section 13, pp 107-8, # 1, 3, 7, 8, 9, 10.
- Curtis, Section 15, pp 129-30, # 1b, 2, 6, 8, 9.
-
Tuesday, March 29 (Determinants)
- Curtis, Section 16, pp 140, # 1a,b, 2, 4. [Note: #4 is by far the most important.]
- Curtis, Section 17, pp 146, # 1, 2.
- Curtis, Section 19, pp 161, # 6.
-
Tuesday, April 5 (Determinants and polynomials)
- Curtis, Section 19, pp 160-1, # 4, 7, 8.
- Curtis, Section 20, pp 175, # 2, 3, 5, 6, 7.
-
Tuesday, April 12 (Complex numbers, minimal polynomials, eigenvectors)
- Curtis, Section 21, pp 182, # 3, 4, 5.
- Curtis, Section 22, pp 192-3, # 3, 4, 8, 9, 10.
-
Tuesday, April 19 (Direct sums, primary decompositions, diagonalizability)
- Curtis, Section 23, pp 201, # 1, 2, 4, 5, 6.
- Curtis, Section 24, pp 215, # 1, 2, 4, 5.
-
Tuesday, April 26 (Elementary divisors, companion matrices, rational forms)
- Curtis, Section 24, pp 215-16, # 6, 7, 8, 9.
- Curtis, Section 25, pp 225-26, # 1, 2, 3, 4, 6.
-
Tuesday, May 3 (Quotients and duality)
- Curtis, Section 26, pp 236, # 2, 3, 4.
- Curtis, Section 27, pp 243, # 3, 5, 6, 7, 8.