Instructor: Dr. Madnick (jmadnick [at] uoregon [dot] edu)
Textbook: Linear Algebra and its Applications (6th edition)
Grades: Posted on Canvas
Lectures: 248 Gerlinger Hall
MTWF: 9:00 - 9:50
Office Hours:
Tue Mar 19: 5:00 pm - 6:30 pm (UO Annex 220)
Quiz Information
Date: Tue 1/30
Time + Location: Our classroom during lecture
Content
Lectures 1-9 (i.e., Weeks 1, 2, 3)
Emphasis on span, linear independence, basis, and dimension.
Structure
#1. [9 pts] State definitions.
#2. [7 pts] Solve a linear system, expressing the solution set as a span.
#3. [7 pts] Problem about span.
#4. [7 pts] Problem about linear independence / dependence.
#5. [7 pts] True/False.
Expectations: To score well, a student should:
Know all the definitions and theorems (i.e., have them memorized).
Be able to solve all the problems from Lectures 1-9 (Units A and B)
Be able to solve all the problems from PSets 1 and 2.
Have a solid conceptual understanding of the definitions and theorems from Lectures 1-9. You can strengthen conceptual understanding by asking yourself lots of "what if?" questions. (If you don't know what this means or how to do it, ask me.)
Midterm 1 Information
Date: Tue 2/6 and Wed 2/7
Time + Location: Our classroom during lecture
Content
Lectures 1-11
Unit A + Unit B + Matrix-Vector Products & Existence Theorem (in Unit C)
Not on Midterm 1: Translation Theorem, Uniqueness Theorem
Structure for Tuesday exam
#1. [9 pts] State definitions.
#2. [7 pts] Solve a linear system, expressing the solution set as p + span.
#3. [7 pts] Problem about linear independence.
#4. [6 pts] Abstract problem about span and linear independence.
Structure for Wednesday exam
#5. [4 pts] Matrix-vector products.
#6. [8 pts] Problem about span and basis.
#7. [6 pts] Problem about linear subspaces.
#8. [8 pts] True/False.
Advice for success:
Work through the Midterm Practice Problems before the lecture on Mon 2/5
Know all the definitions and theorems (i.e., have them memorized).
Be able to solve all the problems from Lectures 1-11 (Units A, B, and part of Unit C).
Be able to solve all the problems from PSets 1, 2, 3. (Also good practice: On PSet 4: Problems 1, 2, 3)
Strengthen your conceptual understanding by asking yourself lots of "what if?" questions. (If you don't know what this means or how to do it, ask me.)
Midterm 2 Information
Date: Tue 2/27 and Wed 2/28
Time + Location: Our classroom during lecture
Content
Lectures 11-19
Unit C + Interlude + Unit D
Not on Midterm 2: Inverse of a matrix.
Structure for Tuesday exam
#1. State definitions.
#2. Find basis of null space and column space.
#3. Find dimension of span of a set of vectors.
#4. Find matrix representation of a linear transformation.
Structure for Wednesday exam
#5. Matrix products
#6. Injectivity and surjectivity of linear transformations.
#7. Geometric / conceptual question about null and column spaces.
#8. Always / Sometimes / Never
Advice for success:
Work through the Midterm Practice Problems before the lecture on Mon 2/26
Know all the definitions and theorems (i.e., have them memorized).
Be able to solve all the problems from Lectures 11-19 (Units C and D, except for inverses and invertibility.)
Be able to solve all the problems from PSets 4, 5, 6. (Also relevant: PSet 7: #1(a)-(b).)
Strengthen your conceptual understanding by asking yourself lots of "what if?" questions. (If you don't know what this means or how to do it, ask me.)
Final Exam Information
Thursday March 21
10:15 am - 12:15 pm
Location: Our classroom (248 Gerlinger)
Content
Lectures 19-28
Units D, E, F
Emphasis on Unit F
Structure
#1. (Unit F) Coordinate representations.
#2. (Unit E) Determinants: geometry problem.
#3. (Unit D and F) Matrix representation of a linear transformation.
#4. (Unit F) Linear subspaces.
#5. (Unit D and F) Linear transformations: theoretical problem.
#6. (Unit D) Linear transformations: geometry problem.
#7. (Unit E) Determinants: theoretical problem.
#8. (Unit F) Linear independence and dependence.
Note 1: There won't be a question asking you to state the definitions. However, knowledge of the definitions will be necessary to solve many of the problems on the exam.
Note 2: Don't worry about change-of-basis: it won't be examined. You also don't need to memorize the definition of "vector space."
Tips for studying
Know all the definitions and theorems (i.e., have them memorized).
Know the algebraic properties of determinants, and also those of transposes.
Be able to solve all the problems from Lectures 19-28.
Be able to solve all the problems from PSets 7, 8, 9.