MATH 3130, section 001: linear algebra
Prof. Monk
Fall 2009
Web page updated Nov. 18, 09: solutions, assignment 11.
Files to download are in .pdf form.
Syllabus
Assignments
Assignment 1, due Monday, Aug. 31: pages 5-8: 6, 16, 24, 26, 36.
Also, pages 18-24: 8, 18, 30, 40, 70. (All 10 to
be turned in.) Similar odd-numbered exercises, with solutions in the back
of the book: pages 5-8: 7, 15, 27, 25, 35; pages 18-24: 9, 19, 31, 41, 73.
(These are not to be turned in.) [Third edition: the second group of exercises
is on pages 20-26. Exercise 70 is a new one for the fourth edition, and reads
as follows:
"A rooster is worth five coins, a hen three coins, and 3 chicks for one
coin. With 100 coins we buy 100 of them. How many roosters, hens, and chicks
can we buy?" (From the "Mathematical Manual" by Zhang Qiujian, Chapter 3,
Problem 38, 5th century A.D.)]
Assignment 2, due Wednesday, Sept. 9: pages 33-37: 4, 18, 30, 44, 58; and
pages 50-53: 6, 14, 34, 50, 52. (All
to be handed in.) Similar odd numbered exercises, with solutions in the
back of the book: pages 33-37: 3, 19, 29, 47, 59; and pages 50-53: 7, 15,
33, 49, 53. (None of these to be handed in.) [Third edition: the exercises are
found on pages 35-38 and 51-54.]
Assignment 3, due Wednesday, Sept. 16: pages 65-69: 4, 10, 20, 28,
40; and pages 77-79: 14, 20, 28, 32, 38. (All to be handed in.)
Similar odd numbered exercises,
with solutions in the
back of the book: pages 65-69: 7, 9, 19, 27, 49; and pages 77-79: 13, 21, 27,
39. (None of these to be handed in.) [Third edition: the first group of
exercises is found on pages 66-70. The second group is as follows:
p. 89 #14; p. 93 #76; p. 93 #64; p. 90 #39; and the last one is new: For $A$
as in example 2.1.5 on page 46, compute A, A^2=AA, A^3=AAA, etc., describe the
pattern that emerges, and use this description to find A^{1001}.]
Assignment 4, due Wednesday, Sept. 23: pages 88-98: 10, 30, 42, 66, 76; and
pages 110-113: 12, 26, 30, 42, 44.
(All to be handed in.)
Similar odd numbered exercises,
with solutions in the
back of the book: pages 88-98: 7, 31, 39, 67, 79; and pages 110-113: 11, 25,
31, 45, 47.
(None of these to be handed in.) [Third edition: the first group of exercises
corresponds to page 76 #10; page 76 #30; page 77 #42; page 89 #34; page 90 #44.
The second group of exercises is found on pages 109-112.]
Assignment 5, due Wednesday, Sept. 30: pages 121-123: 2, 18, 38, 48, 56; and
pages 133-137: 18, 24, 32, 44, 78.
(All to be handed in.)
Similar odd numbered exercises,
with solutions in the
back of the book: pages 121-123: 3, 19, 39, 49; and pages 133-137: 17, 25, 31,
45, 81.
(None of these to be handed in.) [Third edition: the exercises are on the same
pages, except for the last two. #78 in the fourth edition is the same as #58
in the third edition. #44 in the fourth edition is new; it is as follows:
A cubic is a curve in R^2 which can be described by and equation of the form
f(x,y)=c_1+c_2x+c_3y+c_4x^2+c_5xy+c_6y^2+c_7x^3+c_8x^2y+c_9xy^2+c_{10}y^3=0.
Find all cubics through the points (0,0), (1,0), (2,0), (3,0), (0,1), (0,2),
(0,3), (1,1).]
Assignment 6, due Wednesday, Oct. 7: pages 147-150: 10, 22, 38, 50, 56;
and pages 163-164: 10, 26, 40, 54, 58.
(All to be handed in.)
Similar odd numbered exercises,
with solutions in the
back of the book: pages 147-150: 11, 23, 39, 49, 63; and pages 163-164: 11,
25, 39, 53, 52.
(None of these to be handed in.) [Third edition: pages 146-150: as in fourth
edition; pages 162-163: as in the fourth edition.]
Assignment 7, due Wednesday, Oct. 14: pages 170-172: 8, 42, 60, 68, 76; and
pages 181-184: 10, 28, 54, 62, 70. (All
to be handed in.) Similar odd numbered exercises, with solutions in the back
of the book: pages 170-172: 11, 33, 55, 67, 77; and pages 181-184: 11, 33, 55,
63, 69. (None of these to be handed in.)
[Third edition: pages 169-171 and pages 180-183:
as in the fourth edition.]
Assignment 8, due Wednesday, Oct. 21: pages 199-202: 10, 16, 22, 24, 36 (hint:
try to use the equality condition in Theorem 5.1.11); and pages 209-210: 2,
16, 34, 40, 44 (hint: show that it is not possible if n is less than m
(easy), but it is
possible for m at most n, by induction on m (not so easy)). (All of these to
be handed in.)
Similar odd numbered exercises, with solutions in the back
of the book: pages 199-202: 11, 17, 23, 27, 33; and pages 209-210: 3, 17, 33,
41, 45. (None of these to be handed in.) [Third edition: same.]
Assignment 9, due Wednesday, Oct. 28: pages 218-220: 4, 24, 38, 44, 64; and
pages 229-233: 6, 8, 20, 30, 42. Similar odd numbered exercises, with
solutions in the back of the book: pages 218-220: 3, 25, 37, 45, 65; and pages
229-233: 3, 9, 19, 31, 15. (None of these to be handed in.) [Third edition:
same.]
Assignment 10, due Wednesday, Nov. 4: pages 244-247: 2, 4, 10, 14, 24; and
pages 259-261: 8, 22, 28, 44, 56. (All of these to be handed in.) Similar odd
numbered exercises, with solutions in the back of the book: pages 244-247: 3,
5, 7, 15, 23; and pages 259-261: 9, 21, 27, 43, 57. [Third edition: same,
except for 56 on page 260, which is changed slightly: in the new version, find
d_1,d_2,...,d_7 and then find a formula for d_n in terms of n.]
Assignment 11, due Wednesday, Nov. 11: pages 273-277: 6, 30, 40, 48, 66; and
pages 289-292: 4, 14, 28, 30, 38. (All of these to be handed in.) Similar odd
numbered exercises, with solutions in the back of the book: pages 273-277: 5,
29, 39, 47, 65; and pages 289-292: 3, 13, 29, 31, 37. [Third edition: pages
273-277: number 66 is new; a copy of page 277 in the fourth edition is
here; pages
289-292: same as fourth edition.
Assignment 12, due Wednesday, Nov. 18: pages 305-308: 6, 12, 38, 44, 54; and
pages 317-319: 10, 16, 22, 28, 46. (All of these to be handed in.) Similar odd
numbered exercises, with solution in the back of the book: pages 305-308: 5,
13, 39, 43, 53; and pages 317-319: 11, 17, 23, 29, 47. [Third edition: same]
Assignment 13, due Wednesday, Dec. 2: pages 327-331: 14, 20, 38, 48, 52;
and pages 340-343: 6, 16, 30, 38, 46. (All of these to be handed in.) Similar
odd numbered exercises, with solution in the back of the book: pages 327-331:
13, 19, 39, 47, 53; and pages 340-343: 7, 17, 29, 37, 45. [Third edition: same
except for page 331, no. 52;
here is a
copy of page 331.
Assignment 14, due Wednesday, Dec. 9: pages 353-357: 12, 16, 24, 38(omit part
c), 46; and pages 373-376: 2, 10, 16, 22, 30. (All of these to be handed in.)
Similar odd numbered exercises, with solution in the back of the book: pages
353-357: 11, 15, 23, 39, 45; and pages 373-376: 3, 9, 14, 23, 29. [Third
edition: only page 354, number 16 is new;
here is a
copy of page 354.
Miscellaneous notes
Page 15
Page 18
Page 31
Page 50
Page 58
Page 59
Page 75
Page 82
Page 108
Page 109
Page 126
Page 128
Page 128
Page 140
Page 145
Page 165
Page 180
Page 193
Page 196
Page 216
Page 217
Page 234
Page 255
Page 262
Page 264
Page 267
Page 270
Page 279
Page 280
Index of symbols.
Solutions
Assignment 1
Assignment 2
Assignment 3
Assignment 4
Assignment 5
Assignment 6
Correction to solution of exercise 56, page 149 (assignment 6)
Assignment 7
Assignment 8
Assignment 9
(page 219, exercise 44 has the solution n, not m; 3.3.7 is applied in the last
line to the transpose of A, an mxn matrix)
Assignment 10
Assignment 11
Practice problems 1
Practice problems 2
Test 1
Test 2