Instructor: Christopher Sadowski
Email: csadowski at ursinus dot edu
Office: Pfahler Hall 101L
Office Hours: T, F 10:30-12:00 and by appointment
Text: Linear Algebra and its Applications, Fourth Edition, by David C. Lay
Location: Pfahler Hall 207
Meeting times: Monday, Tuesday, Thursday, and Friday 8:00-8:50 A.M.
Grading:
-10% Homework
-10% Quizzes
-15% Midterm 1
-15% Midterm 2
-15% Midterm 3
-35% Final Exam
Midterms:
Midterm 1 will be on Thursday, 10/2/14.
Midterm 2 will be on Thursday, 10/30/14.
Midterm 3 will be on Tuesday, 11/25/14.
Final Exam will be on Monday, 12/8/14 at 9am in Pfahler 207 (our usual room)
Midterm Averages:
Midterm 1: 73.43
Midterm 2: 80
Midterm 3: 71.4
Final Exam:
Quizzes: Quizzes will be given weekly each Thursday.
Homework: There will be weekly homework assigned, listed here.
Please show all work and explain all reasoning behind your solution. Writing down an answer without an explanation will result in no credit for the problem!
Homework 1, to be handed in 9/4/2014:
Section 1.1: 11, 13, 15, 21
Section 1.2: 1, 3, 11
Section 1.3: 9, 13, 15, 17
There will be a quiz on this material on 9/4/2014.
Homework 2, to be handed in 9/11/2014:
Section 1.4: 12, 17, 19, 22, 26
Section 1.5: 5, 11, 17, 25
Section 1.6: 7
There will be a quiz on this material on 9/11/2014.
Homework 3, to be handed in 9/18/2014:
Section 1.6: 12
Section 1.7: 2, 15, 16, 17, 27, 28
Section 1.8: 4, 7, 19, 24, 30
There will be a quiz on this material on 9/18/2014.
Homework 4, to be handed in 9/25/14:
Section 1.9: 5, 6, 17, 22
Section 2.1: 2, 4, 7, 8, 10, 22
Section 2.2: 2, 7, 19, 31, 33
There will be a quiz on this material on 9/25/14.
Homework 5, to be handed in 10/3/14:
Section 2.3: 4,6,13,14,15,18,28,33
Note: In 28, you may NOT assume that B is invertible! You must show that it has an inverse by using the Invertible Matrix Theorem.
Section 2.4: 5, 10, 25
Section 2.8: 5, 7, 15, 18
Homework 6, to be handed in 10/10/14:
Section 4.1: 1, 2, 5, 7, 11, 12, 13, 20, 21, 22
There will be a quiz on this material on 10/9/14.
Homework 7, to be handed in 10/17/14:
Section 2.9: 9, 10, 11
Section 4.2: 2, 16, 18, 23, 33, 34
Section 4.3: 15, 16, 21, 26
There will be a quiz on this material on 10/17/14.
Homework 8, to be handed in 10/24/14.
Section 4.4: 9, 11, 12, 13, 27, 28, 32
Section 4.5: 4, 5, 7, 12, 13, 14, 21
There will be a quiz on this material on 10/23/14.
Homework 9, to be handed in 10/31/14.
Section 3.1: 1, 3, 9, 14, 16
Section 3.2: 5, 8, 10, 12, 27, 29, 34, 40abc
Section 3.3: 2, 8, 19, 27
Homework 10, the be handed in 11/7/14.
Section 5.1: 6, 7, 9, 13, 17, 18, 24, 25, 26
Section 5.2: 2, 10, 11, 12, 16
For the problems in section 5.2, find all eigenvectors for each eigenvalue also.
There will be a quiz on this material on 11/6/14.
Homework 11, the be handed in 11/17/14.
Section 5.3: 2, 3, 6, 11, 12, 13, 14, 25, 27, 32
Section 5.5: 1, 2, 7, 8, 14
There will not be a quiz on this material this week.
Homework 12, to be handed in 11/21/14
Section 6.1: 2, 4, 6, 13, 16, 22, 24, 30, 31
For problem 16, find the orthogonal complement to the subspace spanned by u and v.
There will be a quiz on 5.3, 5.5, and 6.1 on 11/20/14.
Syllabus (subject to change as the course progresses):
Week 1: 8/25 - 8/29
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
Week 2: 9/1 - 9/5
1.4 The Matrix Equation Ax=b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
Week 3: 9/8 - 9/12
1.7 Linear Independence
1.8 Introduction to Linear Transformations
Week 4: 9/15 - 9/19
1.9 The Matrix of a Linear Transformation
2.1 Matrix Operations
2.2 The Inverse of a Matrix
Week 5: 9/22 - 9/26
2.3 Characterizations of Invertible Matrices
2.4 Partitioned (Block) Matrices
2.8 Subspaces of R^n
Week 6: 9/29 - 10/3
2.9 Dimension and Rank in R^n
4.1 Vector Spaces and Subspaces
MIDTERM 1 WILL BE ON THURSDAY, 10/2/14.
Week 7: 10/6 - 10/10
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets and Bases
4.4 Coordinate Systems
Week 8: 10/15 - 10/16
4.4 Coordinate Systems (continued)
4.5 Dimension of a Vector Space
Week 9: 10/20 - 10/24
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule
Week 10: 10/27 - 10/31
5.1 Eigenvalues and Eigenvectors
5.2 The Characteristic Equation
MIDTERM 2 IS ON THURSDAY, 10/30/14.
Week 11: 11/3 - 11/7
5.3 Diagonalization
5.5 Complex Eigenvalues
Week 12: 11/10 - 11/14
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
Week 13: 11/17 - 11/21
6.2 Orthogonal Sets
6.3 Orthogonal Projections
Week 14: 11/24 Midterm 3 (tentative)
Week 15: 12/1 - 12/5
6.4 The Gram-Schmidt Process
6.5 Least-Squares