Homework Assignment 11
Assigned Fri 04/22. Due Fri 04/29.
1. Let V be an inner product space.
(a) If U V is a subspace, show that U (U ) .
(b) If dim(V ) < , show that U = (U ) .
2. Suppose we want to
21341 Linear Algebra: Final.
Thu 05/05, 2011
This is a closed book test. No calculators or computational aids are allowed.
You have 3 hours. The exam has a total of 9 questions and 90 points.
You m
Math 341 Final.
Tue, Dec 15, 2009
Time: 50 mins
Total: 80 points
This is a closed book test, and your are not allowed to use calculators or other computational aids. You may use any result from class/
Math 341 - Linear algebra
FINAL EXAM
Monday Dec. 13, 2010
1. (2/100) Name:
2. (10/100) Suppose that V is a vector space with complex inner product , . Prove that for all v, w V
v, w =
where i is the i
Homework Assignment 10
Assigned Fri 04/08. Due Fri 04/22.
This homework is a double homework in order to avoid a conict with Spring carnival. It will
count as two homeworks for your grade. The second
21341 Linear Algebra: Midterm 1.
Wed 02/09
This is a closed book test. No calculators or computational aids are allowed.
You have 50 minutes. The exam has a total of 5 questions and 50 points.
You
Homework Assignment 9
Assigned Fri 04/01. Due Fri 04/08.
1. (Optional) Let M be an upper triangular matrix. Show that the eigenvalues of M are exactly the
diagonal entries of M . [I stated, but did no
Math 341 - Linear algebra
Midterm 2 (A)
Wed. Oct. 27, 2010
1. (2/50) Name:
2. (10/50) Suppose that V is vector space with (real) inner product , . Prove that for all u, v V
u, v =
1
[ u+v
4
2
u v 2 ]
Solutions to Homework Assignment 12
Assigned Fri 04/29. Due never.
2. Let V be a nite dimensional inner product space. Show that T L(V, V ) is
positive if and only if there exists S L(V, V ) such that
21341 Linear Algebra: Midterm 1.
Wed 03/23
This is a closed book test. No calculators or computational aids are allowed.
You have 50 minutes. The exam has a total of 5 questions and 50 points.
You
Math 341 Syllabus and Lecture schedule.
L10, Wed 02/02.
Gautam Iyer, Fall 2010
L1, Mon 01/10.
Error correcting codes.
F = cfw_0, 1, choose a, b, c F .
Pick cfw_v1 , v2 , v3 F n , and transmit the
LINEAR ALGEBRA HOMEWORK 4 SOLUTIONS
JAMES CUMMINGS
This homework is due by class time on Friday 21 February. You may not collaborate. Ask me if you nd that a question is unclear or suspect that you ha
LINEAR ALGEBRA HOMEWORK 4
JAMES CUMMINGS
This homework is due by class time on Friday 21 February. You may not collaborate. Ask me if you nd that a question is unclear or suspect that you have
found a
LINEAR ALGEBRA HOMEWORK 3 SOLUTIONS
JAMES CUMMINGS
(1) Let V be a vector space over a eld k and let : V V be a linear
transformation. We dene powers of by the recursive denition 1 =
, t+1 = t (if you
LINEAR ALGEBRA HOMEWORK 1 SOLUTIONS
JAMES CUMMINGS
This homework is due by class time on Monday 27 January. You may not
collaborate. Ask me if you nd that a question is unclear or suspect that you hav
LINEAR ALGEBRA HOMEWORK 1
JAMES CUMMINGS
This homework is due by class time on Monday 27 January. You may not
collaborate. Ask me if you nd that a question is unclear or suspect that you have
found a
LINEAR ALGEBRA HOMEWORK 2 SOLUTIONS
JAMES CUMMINGS
Observation: A linear map is injective if and only if its nullspace is zero,
because (v1 ) = (v2 ) if and only if v1 v2 is in the nullspace.
(1) Let
LINEAR ALGEBRA HOMEWORK 3
JAMES CUMMINGS
This homework is due by class time on Friday 14 February. You may not collaborate. Ask me if you nd that a question is unclear or suspect that you have
found a
LINEAR ALGEBRA HOMEWORK 2
JAMES CUMMINGS
This homework is due by class time on Friday 7 February. You may not collaborate. Ask me if you nd that a question is unclear or suspect that you have found
a
LINEAR ALGEBRA HOMEWORK 5
JAMES CUMMINGS
You may consult any printed or online source, but must cite all sources other
than the textbook. Contact me if you think you have found a typo or do not
unders
Math 341 - Linear algebra
Midterm 1 (A)
Wed. Sept. 22, 2010
1. (2/50) Name:
2. (10/50) Suppose that R is such that 2 Q. Let
F := cfw_a + b : a, b Q.
1
Prove that if x F and x = 0 then x F . Note: The
Homework Assignment 1
Assigned Mon 01/10. Due Fri 01/14.
1. Suppose F (with binary operations +, ) is some eld, and assume all quantities referenced in this
problem are elements of F . Do this problem
10
Math 341 Homework (Fall 2009)
Assignment 14: Assigned Sat 12/05. Due Never.
1. (a) Show that (T ) = T .
(b) Show that (ST ) = T S .
2. Let S, T L(V, V ) be such that ST = T S.
(a) If S and T are di
Math 341 Homework (Fall 2009)
9
Assignment 13: Assigned Wed 11/25. Due Fri 12/04. Last ever
1. The following statements were stated, but not completely proved in class. Prove them.
(a) If v1 , . . .
8
Math 341 Homework (Fall 2009)
Assignment 12: Assigned Wed 11/18. Due Tue 11/24 by 10:00AM
Please note the due date is Tuesday at 10:00AM because there will be no class the Wednesday
before Thanksgiv
Math 341 Homework (Fall 2009)
Assignment 1: Assigned Wed 08/26. Due Wed 09/02
1. Suppose F (with binary operations +, ) is some eld, and assume all quantities referenced in this
problem are elements o
LINEAR ALGEBRA FINAL: TAKE HOME PART
JAMES CUMMINGS
This part of the nal is due by 8:30am on Mon Dec 18. You may work on it
during any continuous 24 hour period of your choice. You may not collaborate
Math 341 Homework (Fall 2009)
7
Assignment 11: Assigned Wed 11/11. Due Wed 11/18
1. In class we showed that if A is an invertible n n matrix, then |AB| = |A|B| for any n n matrix
B. This problem prove