Homework 1 (due 1/15):
1.2) 1, 3, 4
1.3) 1, 2b, 4, 6, 10
1.4) 1, 5, 12
1.5) 1, 2, 6
Homework 2 (due 1/22):
1.5) 9, 12, 15
2.2) 1, 2, 3, 5, 10, 11, 16
Solution suggestion for 1.5, #12 (page
1,
2).
Sec. 2.2, #17b (page
1,
2).
Homework 3 (due 1/29):
2.2) 4, 6, 7, 9, 17b (mimic proof of Prop. 2)
Solution suggestion for #17b (page
1,
2).
Homework 4 (due 2/5):
2.3) 1, 3, 4, 7 (assigned previous week) and 10, 11, 15
Homework 5 (due 2/12):
2.4) 2, 3, 11, 13, 17
Homework 6 (due 2/19):
2.5) 1a,b 3, 9, 10
Additional exercise: Let V denote the vector space of smooth real-valued
functions spanned by cos(x) and sin(x) and let L denote the linear
transformation mapping V into V given by (L(f))(x) = f(x + y) for some
fixed real number y. Find the matrix representation of L with respect to
the basis {cos(x), sin(x)} of V. (Sorry about the minor notational differences
from the problem specification in class; I don't know how to get the Greek
alphabet and subscripts in HTML.)
Homework 7 (due 2/26):
2.5) 4, 11, 14
3.2) 8a,c
Solution suggestion for 2.5 #14.
Homework 8 (due 3/4):
3.2) 2, 7, 9a
3.3) 1, 5a b e, 19