1
General Information
Course:
Main Lecturer:
Further Lecturers:
Literature:
2
Linear Algebra
Gerold Jäger
Per-Anders Boo, Axel Torshage, Emelie Wibron
Howard Anton, Chris Rorres:
“Elementary Linear Algebra with Supplementary Material”
Course schedule
Date
Mon
Tue
Wed
Thu
Fri
Lectures
Time Room
21/1
22/1
23/1
24/1
25/1
8–10
8–10
8–10
8–10
8–10
HsalA
HsalA
HsalA
HsalA
HsalA
Mon 28/1
Tue 29/1
Wed 30/1
Thu 31/1
Fri 1/2
8–10
Mon
Tue
Wed
Wed
Thu
Fri
4/2
5/2
6/2
6/2
7/2
8/2
Problem Solving Sessions (etc.)
Time Group 1 Group 2 Group 3 Group 4
10–12
MA136
MA146
MA156
MA166
10–12
MA136
MA146
MA156
MA166
HsalA
10–12
MA136
MA146
MA156
MA166
8–10
8–10
8–10
HsalA
HsalA
HsalA
10–12
MA136
MA146
MA156
MA166
8–10
8–10
HsalGa
HsalA
8–10
8–10
9–13
Pre-exam
S305b
S306b
A208c
4 lab supervision sessions 1d
MA136
MA146
MA156
MA166
4 lab supervision sessions 2e
MA35
MA121
HsalA
10–12
13–17
10–12
13–17
Mon
Tue
Wed
Thu
Fri
11/2
12/2
13/2
14/2
15/2
8–10
HsalA
10–12
MA136
MA146
MA156
MA166
8–10
8–10
8–10
HsalA
HsalA
HsalA
10–12
MA136
MA146
MA156
MA166
Mon
Tue
Wed
Thu
Fri
18/2
19/2
20/2
21/2
22/2
8–10
8–10
8–10
HsalA
HsalA
HsalA
10–12
MA136
MA146
MA156
MA166
10–12
MA136
MA146
MA156
MA166
16–22
Exam ÖP4 & ÖP5
Sa 23/3
9–15
First Re-exam ÖP4
Thu 29/8
9–15
Second Re-exam ÖP7
a
Room located in Humanisthuset.
Room located in Samhällsvetarhuset.
c
Room located in Teknikhuset.
d
Rooms for lab supervision session 1: MA141, MA151, MA316, MA326.
e
Rooms for lab supervision session 2: MA141, MA316, MA326, MA416.
b
1
More exactly:
• The lectures will start at 8.15.
• The problem solving sessions will start at 10.30.
• The labaration sessions will start at 13.15.
3
4
Plan for the Course
Lecture
Date
Section
1
2
3
4
5
Mo 21/1
Tue 22/1
Wed 23/1
Thu 24/1
Fri 25/1
1.1
1.3
1.5
1.7
2.2
6
7
8
9
Mon 28/1
Wed 30/1
Thu 31/1
Fri 1/2
3.1 + 3.2
3.3 + 3.4
3.5
Repetition
3.1:3,5,7,9,13,25,27,31 + 3.2:1,3,5,7,9,11,13,15,17,23,25
3.3:1,3,5,7,9,11,15,17,19,21,25,29,33,37 + 3.4:1,7,9,15,17,21,25
3.5:1,3,7,13,15,17,19,25,29 + Supplementary Exercises 3:23,25
10
11
12
13
Tue 5/2
Wed 6/2
Thu 7/2
Fri 8/2
4.1 + 4.2
4.3 + 4.4.
4.5 + 4.6
4.7 + 4.8
4.1:1,3,5,7,9 + 4.2:1,3,7,9,11,13,15
4.3:1,3,5,7,9,19 + 4.4:1,3,4,7ab,9a,11,15
4.5:1,3,7,9,15 + 4.6:1,3,5a,7,9
4.7:3abe,5b,7ac,11ab + 4.8:1,2ac,3ac,5,7abc,9,13
14
15
16
17
Mon 11/2
Wed 13/2
Thu 14/2
Fri 15/2
4.9 + 4.10
5.1 + 5.2
6.1 + 6.2
6.3 + 6.4
4.9:1,3,9,11,13,15,17,19 + 4.10:1,3,5,7,9,11,13,23
5.1:1,3ab,5ab,7acf,9a,11a,15 + 5.2:3,5,7,9,15,19,23
6.1:1,5,7,9,11a + 6.2:1bd,3b,7,9,11ab,13,15
6.3:3ab,5,7ab,9a,15a,21a,23 + 6.4:1,3,5a
18
19
20
Mon 18/2
Tue 19/2
Wed 20/2
7.1 + 7.2
7.3
Repetition
7.1:3acd,5,7,13 + 7.2:3,5,7
7.3:3,5,7,11,13,15
+
+
+
+
+
1.2
1.4
1.6
2.1
2.3
Recommended Exercises
1.1:1,6,9,11,13 + 1.2:1,3,5,7,13,21,25
1.3:1,3bgj,5adf,7bc,11,17 + 1.4:5,7,11,12,22,28,39
1.5:1,3,7,11,17,25,27 + 1.6:3,5,9,15,19
1.7:5,11,17,19,21,29,31,35 + 2.1:1,3,5,17,21,23,25,27,29,31,33
2.2:13,15,29,35 + 2.3:5,9,11,17,19,27,29,31
Group Membership
Problem
Lab
Program
solving
supervision
Fristående
Group 1
Session 1
ET (names A–H )
Group 1
Session 1
ET (names I–Å)
Group 2
Session 1
TF (names A–L)
Group 3
Session 2
TF (names M–Å)
Group 4
Session 2
2
5
Examination Rules
The evaluation of this course is based on three parts (see Section 2 for the dates and times):
• Computer Lab: To pass the computer lab, a written report is expected regarding a lab exercise.
The deadline for handing in the lab reports is on February 15.
• Pre-exam: The pre-exam is written on February 4 within 4 hours and covers the first half of the
course, i.e., chapters 1 to 3 of the book. You can reach maximum 4 points in this pre-exam which
can be added to the result of the exam.
• Exam: The exam is written on February 22 within 6 hours and covers the whole course. You can
reach maximum 24 points in this exam (possibly plus 4 extra points from the pre-exam).
Two re-exams are scheduled: one for March 24 and the other for August 29.
For passing the course a minimum of 12 points is required. The grades are as follows:
• The grade 5 requires at least 22 points.
• The grade 4 requires at least 17 points.
• The grade 3 requires at least 12 points.
6
Relevant Proofs
The following proofs are relevant for the exam. You should have completely understood them, and you
should be able to reproduce them.
Theorem
Page
Theorem 1.4.6
Page 45
Theorem 1.6.1
Page 60
Theorem 3.2.1(c)
Page 131
Theorem 3.2.5
Page 138
Theorem 3.4.4
Pages 158+159
Theorem 4.2.4
Page 187
Theorem 4.4.1
Pages 204+205
Theorem 5.2.1
Pages 306+307
Theorem 6.3.2
Pages 354+355
Theorem 7.1.1 ((a) ⇔ (b))
Page 390
3
7
Mistakes in Answers in the Book
Exercise
Correct Solution
1.7.11
3.2.3(d)
Diagonal element a33 of A5 is 5−k
√
√
17 − 26
√
401
3.2.9(a)
u ◦ u = 14
3.2.23(a)
cos(θ) =
3.3.5
√1 (1, −1, 1)
3
3.3.33
1
4.2.1
(a),(c),(d),(e)
4.2.3
(a),(b),(d)
4.2.9
(a),(d)
4.5.3
Basis:
4.6.9(b)
[w]B = (9, −9, −5)
4.8.2(a)
rank(A) = 3, nullity(A) = 0
4.8.9
6.4.5(b)
b1 = b4 − b5 , b2 = 12 b4 , b3 = 2b4 − 3b5
4
1
2
e = 21
, − 21
, 21
7 21
28
e = − 35
51 , 51 , 51 , − 51
7.1.3
(a),(b),(d),(e),(f) and A = A−1
3.2.3(b)
6.4.5(a)
√1 ,
2
i.e., θ = 45◦
(− √13 (1, −1, 1) is also possible)
1
3 , 1, 0, 0
, − 61 , 0, − 14 , 1
4
, Dimension: 2