 Instructor: Anatolii Grinshpan
Office hours:  W 10-11 and F 11-1, Library Learning Terrace.

Week 1. Introduction to the course. Gaussian elimination. Leading and free variables.

Reduced echelon form. Rank. Example. Tall, long, square.

Reading: 1.1, 1.2. Homework 1. Uniqueness of RREF.

Week 2. Quiz 1 (Gauss-Jordan elimination). Vector arithmetic. Matrix-vector product.

Homogeneous and nonhomogeneous systems: the structure of solutions.

Matrices as linear transformations. Reading: 1.3. Homework 2.

Week 3. Quiz 2 (matrix-vector product). Linear transformations.

Projections, reflections, rotations and their matrices. Orthogonal projection in the plane.

Week 4. Matrix multiplication. Elementary matrices. Dihedral group. Quiz 3 (linear transformations).

One-to-one and onto linear transformations. Matrix inversion. LU example.

Reading: 2.3, 2.4. Homework 5. Homework 6.

Week 5. Midterm 1 (weeks 1-4). Block multiplication and inversion. Kernel and image of a matrix.

Span of vectors. Linear dependence and independence.

Reading: 3.1, 3.2. Homework 7. Homework 8.

Week 6. Subspaces associated to a matrix. Quiz 4 (kernel and image). Characterizations of independence.

Basis and dimension. Basis for the kernel and basis for the image. Rank-nullity theorem.

Reading: 3.2, 3.3. Homework 9. Notes on bases.

Week 7. Coordinates. Matrix of a linear transformation with respect to a given basis.

Examples. Transpose. Orthonormal bases.

Reading: 3.3, 3.4, 5.1. Homework 10.

Week 8. Quiz 5 (matrix in a given basis). Orthogonal complement. Orthogonal projection onto a subspace.

Example. Gram-Schmidt process. Orthogonal transformations.

Reading: 5.1-5.3. Homework 11. Homework 12.

Week 9. Midterm 2 (weeks 5-8). Thanksgiving break.

Week 10.  Least squares solutions. Determinants. Cramer’s rule.

Eigenvalues and eigenvectors. Examples.

Reading: 6.1-6.3. Homework 13.

Week 11.  Quiz 6 (determinants). Eigenspaces and eigenbases. Diagonalization.

Reading: 7.1-7.3. Homework 14. Homework 15.

Practice quizzes: Set 1 Set 2 Set 3 Set 4 Set 5 Set 6.

Dec 13.  Office hours: 1-3 (Library Terrace).

Dec 14.  Questions session: 12-2, Disque 108.

Dec 15.  Final exam: 10:30-12:30, Stratton 113.