# Math 201 – Linear Algebra, Fall 2015

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.

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).

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.

Week 6. Matrix inversion. Dihedral group. Block multiplication and inversion.

Quiz 3 (matrix multiplication). Span of vectors. Image and kernel of a matrix.

Week 7. Quiz 4 (matrix inversion). Vector relations. Linear dependence and independence. Subspaces. Basis and dimension.

Basis for the kernel and basis for the image. Subspaces associated to a matrix.

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).

Transpose. Orthonormal bases. Orthogonal projection onto a subspace. Example. Determinants.

Reading: 5.1, 6.1, 6.2. Problems. Problems.

Week 10. Thanksgiving break.

Week 11. Eigenvalues and eigenvectors. Quiz 6 (eigenvalues).  Cross-product transformation.

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.