Instructor: Anatolii Grinshpan
Office hours: TWR 3-4, Korman 249.
Week 1. Introduction to the course. Gaussian elimination. Leading and free variables.
Reduced echelon form. Rank. Example.
Reading: 1.1, 1.2. Problems.
Week 2. Quiz 1 (Gaussian elimination). Homework discussion. Tall, long, square.
Algebra with vectors: addition, scaling, linear combinations, dot product.
Week 3. Homogeneous and nonhomogeneous systems. The structure of solutions.
Matrix-vector product and its properties. Uniqueness of RREF. Quiz 2 (matrix-vector product).
Reading: 1.3. Problems.
Week 4. Linear transformations, Projections, reflections, rotations and their matrices.
Week 5. Questions session: Oct 19, 5-6:30PM, Curtis 457. Midterm 1 (weeks 1-4).
Properties of matrix multiplication. Elementary matrices. Invertible transformations.
Reading: 2.3. Problems.
Week 6. Matrix inversion. Dihedral group. Block multiplication and inversion.
Quiz 3 (matrix multiplication). Span of vectors. Image and kernel of a matrix.
Reading: 2.4. Problems.
Week 7. Quiz 4 (matrix inversion). Vector relations. Linear dependence and independence. Subspaces. Basis and dimension.
Week 8. Quiz 5 (linear independence). Rank-nullity theorem. Coordinates.
Matrix of a linear transformation with respect to a given basis.
Week 9. Questions session: Nov 16, 5-6:30PM, Curtis 457. Midterm 2 (weeks 5-8).
Week 10. Thanksgiving break.
Eigenspaces. Diagonalization. Examples.
Dec 7. Questions sessions: 12-2, Peck 219, and 5-6:30, Randell 327.
Dec 9. Final exam (all lectures): 1-3 PM, Randell 121.