Math 261 - Linear Algebra I, Spring 2020

First Exam: 17 March, 2020, 17:40

Second Exam: 14 April, 2020, 17:40

Final Exam: TBA

Textbook: Linear Algebra, S.H. Friedberg, A.J. Insel & L.E Spence, Fourth Edition, Prentice Hall, 1994.

Tentative Course Outline:
Week 1: Vector Spaces, Subspaces, Sums and Direct Sums of Subspaces
Week 2: Linear Combinations and Linear Equations, Linear Dependence and Linear Independence
Week 3: Bases and Dimension, Quotients Spaces
Week 4: Linear Transformations, Null Spaces and Ranges
Week 5: The Matrix Representation of a Linear Transformation, Composition of Linear Transformations and Matrix Multiplication
Week 6: Invertibility and Isomorphisms
Week 7: The Change of Coordinate Matrix, Dual Spaces
Week 8: Elementary Matrix Operations and Elementary Matrices, The Rank of a Matrix and Matrix Inverses
Week 9: Systems of Linear Equations - Theoretical Aspects
Week 10: Systems of Linear Equations - Computational Aspects
Week 11: Determinants of Order 2, Determinants of Order n
Week 12: Properties of Determinants
Week 13: A Characterization of the Determinant

Suggested Problems:
Section 1.2: 1,3,4,7,13,14,18,19,21.
Section 1.3: 1,3,5,6,8,9,11,15.
Section 1.4: 1,2,3,5,10,13.
Section 1.5: 1,3,7,8,9,13,14,15.
Section 1.6: 1,2,7,11,14,15,20.
Section 2.1: 1,2,4,5,9,10,11,14,17,22.
Section 2.2: 1,2,3,5,8,13,16.
Section 2.3: 1,2,3,12,15,18.
Section 2.4: 1,2,3,4,5,6,9,10,14,17,19,20.
Section 2.5: 1,2,3,4,5,6,7,8,13.
Section 2.6: 1,2,3,4,6,8,9,13,14,15,16.
Section 3.1: 1,2,3,8,9.
Section 3.2: 1,2,3,4,5,6,7,14,15,17,21.
Section 3.3: 1,2,3,4,6,7,8,10.
Section 3.4: 1,2,3,4,5,9,12.
Section 4.1: 1,3,4,6,10.
Section 4.2: 1,3,4,7,8,21,25,28.
Section 4.3: 1,7,8,10,11,12,13,16,20,21,23,26,27.
Section 4.5: 1,15,16.

Office Hours: Tuesdays 14:40 - 15:30, Wednesdays 08:50 - 09:40, M238.

Grading: There will be two midterm exams each of weight 30% and a final exam of weight 40%. One make-up exam will be offered after the final exam for those who have (for a good reason) missed an earlier exam.