Math 159: Problem Set 8
Due Friday, November 20
Chapter 2:
(5 each) Exercise 2.2.2
(10 each) Exercise 2.2.3
(10) Prove the theorem from class saying that for finite dimensional vector
spaces V and W , V
= W if and only if dim V = dim W .
(10) Exercis

Math 159: Problem Set 1
Due Friday, October 2
Chapter 1:
(5 each) Exercises 1.2.1 1.2.4
(5) Prove that A B = B A.
(5) Prove that A \ B and B \ A are disjoint.
(5) Solve (with proof of course!) A \ B = B \ A. In other words, state the
relationship betw

Math 159: Problem Set 9
Due Wednesday, December 2
Determinants:
(10 each) Prove parts (C) and (D) of the theorem from class.
(10) Prove that the determinant function defined in the theorem from class
satisfies Axiom 1) for determinants.
(10) Prove det(

Math 159: Problem Set 3
Due Friday, October 16
Chapter 1:
(5) Prove that the relation dened in Example 1.6.5 is an equivalence
relation.
(5) Exercise 1.6.14: Prove that if X is a union of pairwise disjoint subsets, then the containment of two elements i

Math 159: Problem Set 2
Due Friday, October 9
Chapter 1:
(5 each) Exercises 1.4.10: (i) (iii)
(5) Let A = cfw_a, b, c and B = cfw_1, 2. Determine all of the functions from
A to B.
(10) Exercise: 1.7.9
(10) Show that f 1 is a function. (Recall that f i

Math 159: Problem Set 6
Due Friday, November 6
Chapter 3:
(5 each) Exercise 3.6.24 (iii) - (viii)
(10) Exercise 3.6.25
(20) Exercise 3.6.32
Chapter 2:
(5) Prove that for any eld F the zero vector space given by V = cfw_0
is a vector space. (Of course,

Math 159: Problem Set 7
Due Friday, November 13
Chapter 2:
(5 each) Exercise 2.1.14 (i), (iii)
(10 pts. for each vector space) For each of the three vector spaces dened
in Problem Set 6 (V1 , V2 , V3 ) nd the following: A set that of vector(s)
that span