Linear Algebra (Math 220)
Assignments
Spring Semester, 2003
Assignments are listed by the date due.
PDF and DVI (requires
TeX software) versions of this
page are available for printing.
Most of these assignments are simply exercises designed to prepare you
for the quizzes and the written assignments. Those which are to be
submitted as written assignments are so labeled. While you may find it
helpful to discuss the exercises with others, no collaboration is permitted
on the written assignments.
 Wed., May. 14:

Final Examination, 3:30  5:30
 Tue., May. 13:

Office Hours : 2:30  3:30
 Mon., May. 12:

Office Hours: 12:30  1:30
 Fri., May. 9:

Office Hours: 3:00  4:00
 Mon., May. 5:

Review Session: bring questions
 Fri., May. 2:

Review Session: bring questions
 Wed., Apr. 30:

Affine Maps

Definition.
If V is a vector space,
a translation t : V > V is a map that is given by
t(x) = x + a for some a in V and all x in V.

Definition.
If V is a vector space,
an affine map f : V > V is a map that may be written
as the composition t \circ l where l : V > V is a linear
map and t : V > V is a translation.
Note that saying
f = l \circ t
i.e., f(x) = l(x + a) for some a in V,
rather than
f = t \circ l,
i.e., f(x) = l(x) + a for some a in V,
would change the definition of affine map.
Exercises:
Find an affine map f of R^{2} for which
f(0, 0) = (1, 1), f(1,0) = (4, 1), and f(0, 1) = (4, 3).
When f is an affine map, let lambda(f) denote
its linear component. Show that lambda(g \circ h) = lambda(g) \circ
lambda(h).
Show that an affine map f is invertible if and only if
its linear component lambda(f) is invertible.
(Corrected) Show that if f is an invertible affine map of V
and t a translation of V, then f \circ t \circ f^{1} is a
translation.
 Mon., Apr. 28:

Read: § 6.5
Exercises:
 430: 18
 437: 24, 26, 29
 284: 26, 28
 368: 16, 20
 385: 1, 5
 Fri., Apr. 25:

Exercises:
 430: 11
 437: 18
 284: 15  18, 22
 368: 6, 7, 10, 13, 14
 Wed., Apr. 23:

Read: § 6.4
Exercises:
 417: 16  18
 430: 10(f, h, j), 12
 437: 11, 17
 284: 10  12
 368: 2  5
 Mon., Apr. 21:

Read: § 4.4
Exercises:
 417: 12, 15
 429: 7, 9, 10(a, c, e)
 437: 3, 4, 7
 283: 1  3, 5, 7
 Wed., Apr 16  Fri., Apr 18:

University Recess: No class.
 Mon., Apr. 14:

Read: § 8.3
Exercises:
 359: 40
 406: 20, 21, 23
 417: 11, 13, 14
 429: 5, 6
 437: 1
 Fri., Apr. 11:

Read: § 8.2
Exercises:
 359: 38, 39
 406: 11, 12, 18, 19
 417: 4, 6, 7, 9, 10
 429: 3
 Wed., Apr. 9:

Read: § 8.1
Exercises:
 359: 29, 30  35
 395: 16, 18, 19, 20
 406: 6  8, 14, 15
 417: 1, 3
 Mon., Apr. 7:

Exercises:
 349: 33, 34
 359: 23, 24, 26, 28
 395: 15, 21, 23
 406: 3, 5
 Fri., Apr. 4:

Read: § 7.2
Exercises:
 348: 26, 28, 29
 358: 16, 17, 19, 20, 22
 395: 10, 11, 14
 406: 2
 Wed., Apr. 2:

Read: § 7.1
Exercises:
 336: 30, 32, 34
 348: 20, 21, 23  25
 358: 7, 12, 15
 394: 3, 6, 8, 9
 Mon., Mar. 31:

Read: § 6.3
Exercises:
 315: 19, 21, 22, 25, 26
 336: 26  29
 348: 8, 9, 11, 12, 18, 19
 358: 1  5, 9, 11
 Fri., Mar. 28:

Read: § 6.2
Exercises:
 301: 38  41
 315: 16  18
 336: 11, 12, 16, 17, 23, 25
 347: 2, 3, 5, 7
 Wed., Mar. 26:

Read: § 6.1
Exercises:
 301: 25, 35
 315: 8, 11, 15
 336: 2  4, 7  9, 15
 Mon., Mar. 24:

Read: § 5.3
Exercises:
 271: 30, 31, 35
 300: 14  16, 30, 31
 315: 3, 5, 9, 13
 325: 6
 Fri., Mar. 21:

Read: § 5.2
Exercises:
 262: 24, 25, 28, 32
 271: 6, 8, 17, 21, 29, 38
 300: 7  9, 19, 23
 315: 1, 4
 Wed., Mar. 19:

Read: § 5.1
Exercises:
 227: 24, 26, 34
 248: 38, 41, 46, 49
 262: 22, 26, 30
 271: 15, 16, 20, 28
 300: 1  5
 Mon., Mar. 17:

Read: § 4.3
Exercises:
 228: 31  33
 248: 8, 9, 16, 17, 20, 21, 25, 33
 261: 4, 8, 13, 15  21
 271: 2, 5
 Fri., Mar. 14:

Read: §§ 4.1, 4.2
Exercises:
 227: 23
 236: 9, 10, 14, 15
 248: 4, 7, 10  12, 15, 19
 261: 3, 7
 Wed., Mar. 12:

Midterm Test
 Mon., Mar. 10:

Review Session. Bring questions.
Be sure to obtain a copy of the handout (also available as PDF or DVI) that
supplements the class of Fri., Feb 28.
 Recess
 Mar. 1  Mar. 9
 Fri., Feb. 28:

Read: § 3.5
Exercises:
 203: 34, 35, 37, 38, 41, 42
 211: 12, 21
 226: 10  12, 20, 21
 236: 1  8, 11, 12
 Wed., Feb. 26:

Read: § 3.4
Exercises:
 152: 33
 190: 25
 201: 29 32, 40
 211: 6  9, 11, 19
 226: 1  5, 16, 17
 Mon., Feb. 24:

Read: § 3.3
Exercises:
 152: 19, 20, 25, 26, 29, 31
 190: 23, 24
 201: 19  22, 25, 27, 28
 211: 1  5, 10
 Fri., Feb. 21:

Read: § 3.2
Exercises:
 152: 21  24
 189: 3, 16  18
 201: 1  6, 8, 9, 11  14
 Wed., Feb. 19:

Read: § 3.1
Exercises:
 135: 31, 37
 140: 5, 6, 14, 15, 17, 21
 152: 9, 10, 14  16
 189: 1, 2, 9  15
 Mon., Feb. 17:

President's Day Recess: no class
 Fri., Feb. 14:

Read: § 2.3
Exercises:
 100: 45, 46
 135: 24, 25, 27, 28, 32
 140: 7, 10, 11, 13, 18  20
 152: 1  8, 13
 Wed., Feb. 12:

Read: § 2.2
Exercises:
 100: 32, 36, 38, 42, 44
 135: 11, 13, 14, 16, 22, 23, 26, 30
 140: 1  4, 12
 Mon., Feb. 10:

Expect at least one quiz this week.
Read: § 2.1
If you find § 2.1 opaque, it is likely that you have not
fully digested § 1.6.
Exercises:
 86: 33, 34, 38
 100: 26, 27, 29, 31, 34, 35
 134: 1  5, 7, 9, 10, 12
 Fri., Feb. 7:

Exercises:
 68: 35  39, 44, 45, 47, 48
 84: 15, 16, 20, 23, 25  27, 29, 30
 99: 12, 13, 16, 17, 19, 23  25
 Wed., Feb. 5:

Read: § 1.6
Exercises:
 48: 45, 46
 68: 26, 27, 29, 30  34, 43, 56
 84: 9, 10, 11, 13
 99: 1  10
 Mon., Feb. 3:

Read: § 1.5
Exercises:
 46: 24, 36, 39, 41
 68: 11, 12, 23, 25, 42
 84: 6, 7
 Fri., Jan. 31:

Exercises:
 16: 21, 23, 27, 32, 35, 38, 39
 31: 5, 8, 11, 14, 16, 19, 22, 23
 46: 3, 4, 11, 12, 17  19, 23
 Wed., Jan. 29:

Read: Read § 1.3
Exercises:
 68: 3, 4, 5, 7, 8, 9
 Mon., Jan. 27:

Read: §§ 1.1  1.2, 1.4
Exercises:
 15: 6, 10, 21, 25
 31: 4, 11, 12
 68: 2
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