Week 1
☛ Wednesday ☚
Solving systems of linear equations.
Homework due Wednesday
- Reading: Chapter One, Sections I and III.
- Practice problems: Chapter One, Section I: 1.17, 1.22, 1.27, 1.37
(challenge). (Note: do not turn in practice problems.)
☛ Friday ☚
Reduced row echelon form. Wikipedia link:
Gaussian elimination.
Homework due Friday
- Reading: Chapter One, Sections I and III.
- Practice problems: Chapter One, Section I: 2.18, 2.21, 2.24, 2.29, 2.32
(challenge), 3.15, 3.18, 3.25; Section III: 1.8, 1.10, 1.14, 1.15, 2.11,
2.20, 2.24. (Note: do not turn in practice problems.)
Week 2
☛ Monday ☚
Vector spaces.
Homework due Monday
- Reading: Chapter One, Section II.1, Chapter Two, Section I.
- Practice problems: Chapter Two: 1.18, 1.19, 1.22, 1.28, 1.29, 2.20,
2.21, 2.26, 2.29, 2.44.
- Turn in by 1 pm on Tuesday in the folder outside my office:
H02T (tex file: H02T.tex,
solutions: H02Tsol).
☛ Wednesday ☚
Subspaces and spanning sets.
Homework due Wednesday
- Reading: Chapter Two, Section I.2.
- Practice problems: Chapter Two, Section I.1: 1.18, 1.19, 1.22, 1.29,
1.30.
☛ Friday ☚
Linear independence.
Homework due Friday
- Reading: Chapter Two, Section II.1.
- Practice problems: Chapter Two, Section II.1: 1.20, 1.21, 1.23 (b).
- Turn in:
H02F
(tex file: H02F.tex
solutions: H02Fsol).
Week 3
☛ Monday ☚
Linear independence.
Homework due Monday
- Reading: Same as last Friday: Chapter Two, Section II.1.
- Practice problems: Same as last Friday: Chapter Two, Section II.1: 1.20, 1.21, 1.23 (b).
- Turn in by 1 pm on Tuesday in the folder outside my office:
H03T (tex file: H03T.tex
solutions: H03Tsol).
☛ Wednesday ☚
Bases. (Supplement: here is a nice article on
infinite-dimensional vector spaces.)
Homework due Wednesday
- Reading: Chapter Two, III.1.
- Practice problems: Chapter Two, III.1: 18, 19, 20, 21, 23, 29.
☛ Friday ☚
Dimension.
Homework due Friday
- Reading: Chapter Two, III.2.
- Practice problems: Chapter Two, III.2: 16, 18, 22, 26, 27, 34.
- Turn in:
H03F
(tex file: H03F.tex,
solutions: H03Fsol).
Week 4
☛ Monday ☚
Row space and column space
Homework due Monday
- Reading: Chapter Two, III.3.
- Practice problems: 3.17, 3.20, 3.21, 3.23, 3.29.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H04T (tex file: H04T.tex,
solutions: H04Tsol).
☛ Wednesday ☚
Linear transformations.
Homework due Wednesday
- Reading: Chapter Three, II.1.
- Practice problems: Chapter Three, II.1, 1.18, 1.19, 1.22, 1.26, 1.28,
1.32, 1.35, 1.37.
☛ Friday ☚
Range space and nullspace. Rank-nullity theorem.
Homework due Friday
- Reading: Chapter Three, I.1, I.2, II.2.
- Practice problems: Chapter Three, Section II: 2.21, 2.23, 2.24, 2.26,
2.35, 2.37, 2.40.
- Turn in: Midterm 1 due at the beginning of class. To review
for the midterm, please read through all of the lecture notes up through
and including Monday of this week, and review the homework problems
given up through last Friday—the solutions are available through
Moodle. The midterm is closed-book/computers/etc. You should not
consult others about your solutions. You have two hours to complete it
once you have started.
Comments: Please be particularly sure you can solve systems of
linear equations as we have presented it. That means knowing precisely
what constitutes reduced echelon form and after computing it, being able
to express your solution exactly in the two forms presented in the lecture on Friday of Week 1.
Midterm
1 solutions
Week 5
☛ Monday ☚
Isomorphisms.
Homework due Monday
- Reading: Chapter Three, Sections I.1, I.2, II.2.
- Practice problems: Chapter Three, Section I: 1.21, 1.23, 1.30, 1.37,
2.15, 2.19.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H05T (tex file: H05T.tex,
solutions: H05Tsol).
☛ Wednesday ☚
Lines, planes, and hyperplanes: equations and parametrizations.
Homework due Wednesday
- Reading: Chapter One, II.1
- Practice problems: Chapter One, II.1: 1, 2, 3, 4, 5, 6.
☛ Friday ☚
Matrices.
Homework due Friday
- Reading: Chapter Four, IV.1 and IV.2.
- Practice problems: IV.1: 1.8, 1.11; IV.2: 2.14, 2.15, 2.16.
- Turn in:
H05F
(tex file: H05F.tex,
solutions: H05Fsol
).
Week 6
☛ Monday ☚
Matrix inversion.
Homework due Monday
- Reading: Chapter 3, IV.4.
- Practice problems: Chapter 3, IV.4: 4.15,Chapter 3, IV.4: 4, 17, 18,
20, 22, 28, 33, 35,
- Turn in by 2 pm on Tuesday in the folder outside my office:
H06T (tex file: H06T.tex
solutions: H06Tsol).
☛ Wednesday ☚
Matrices and linear transformations.
Homework due Wednesday
- Reading: Chapter Three, III.2.
- Practice problems: 2.12, 2.15.
☛ Friday ☚
Matrices and linear transformations.
Homework due Friday
- Reading: Chapter Three, III.2.
- Practice problems: 2.12, 2.15.
- Turn in:
H06F
(tex file: H06F.tex).
Week 7
☛ Monday ☚
Change of basis.
Homework due Monday
- Reading: Chapter Three, V.1 and V.2.
- Practice problems: V.1: 1.7, 1.9, 1.10; V.2: 2.15, 2.16.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H07T (tex file: H07T.tex).
☛ Wednesday ☚
Determinants.
Note: Substitute the following definition of the determinant for the
one given in the book:
determinant. (The definition given in
the book does not work in a field where 1+1=0.)
Homework due Wednesday
- Reading: Chapter Four, I.1 and I.2.
- Practice problems: I.1: 1.1, 1.2, 1.3.
☛ Friday ☚
The determinant of the transpose of a matrix.
Homework due Friday
- Reading: Chapter Four, I.1 and I.2.
- Practice problems: I.1: 1.6, 1.7, 1.8, 1.9.
- Turn in:
H07F
(tex file: H07F.tex).