Fall 2016 - Math 355 - Homework 1
Due: Friday, August 26th.
You may find it helpful to read Appendix A in the text. Below is a summary.
Definition. A set S is a collection of distinct objects. The obj
Fall 2016 - Math 355 - Homework 2
Due: Friday, September 2nd.
All vector spaces are vector spaces over R, unless explicitly stated otherwise.
(1). (20 points, 1.2.1) Determine whether the following st
Fall 2016 - Math 355 - Homework 3
Due: Friday, September 9th.
All vector spaces are vector spaces over R, unless explicitly stated otherwise.
(1). (21 points, 1.3.1) Determine whether the following st
Fall 2016 - Math 355 - Homework 4
Due: Friday, September 16th.
All vector spaces are vector spaces over R, unless explicitly stated otherwise.
(1). (5 points) Find all solutions to the following syste
Fall 2016 - Math 355 - Homework 7
Due: Friday, October 14th.
(1). Let T : R3 R3 be the identity map, the standard ordered basis of R3 , and
= cfw_(2, 3, 2), (1, 1, 0), (2, 0, 1).
(a) (5 points) Find
Fall 2016 - Math 355 - Homework 1
Due: Friday, August 26th.
You may find it helpful to read Appendix A in the text. Below is a summary.
Definition. A set S is a collection of distinct objects. The obj
Fall 2016 - Math 355 - Homework 2
Due: Friday, September 2nd.
All vector spaces are vector spaces over R, unless explicitly stated otherwise.
(1). (20 points, 1.2.1) Determine whether the following st
1. (5 points each) State whether the following are true or false. If false, give a
counterexample.
a. det(A + B) = det A + det B.
Solution:
1 0 0
False. Counterexample: A = 0 1 0 , B =
0 0 1
But det
1. (5 points each) State whether the following are true or false. If true, say why. If false,
give reasons or give a counterexample.
a. The kernel of a linear transformation is a vector space.
Solutio
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=> -L 5 4 o " t3 where £=[zz
A b
0 3 -5
3 LL47 M:[ 4] and A: -z 4. IS "5? )nHne Flame in
'4- I
ZRI+R2=RL[ l at]
-> O 8 IL
~32l+23=R3 O f? {41
Fall 2016 - Math 355 - Homework 3 Solutions
Due: Friday, September 9th.
All vector spaces are vector spaces over R, unless explicitly stated otherwise.
(1). (21 points, 1.3.1) Determine whether the fo