# Math 201 – Linear Algebra, Winter 2019

Instructor: Anatolii Grinshpan.
Office hours:  MW 12-1 and R 2-3, Math Resource Center.

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

Reduced row echelon form. Rank. Newton interpolation. Tall, long, square.

Week 2. Homework discussion. Quiz 1 (Gauss-Jordan elimination). Kronecker-Capelli theorem.

Vectors and vector arithmetic. Homogeneous and nonhomogeneous systems. Matrix-vector product.

Week 3.  No classes.

Week 4. Linear transformations and matrices. Quiz 2 (matrix-vector product).

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

Week 5.  Matrix multiplication and inversion. Example. Quiz 3 (linear transformations).

Midterm 1 (1.1-1.3, 2.1-2.4).

Week 6.  Span of vectors. Kernel and image of a matrix. Subspaces of the Euclidean space.

Quiz 4 (kernel and image). Vectors relations and row/column operations. Notes. Redundancy and linear independence.

Week 7.  Basis and dimension. Basis for the kernel. Basis for the image. Rank-nullity theorem.

Quiz 5 (linear independence). Coordinates. Matrix with respect to a given basis.

Reading: 3.3, 3.4. Homework 6 (answers). Change of basis in the plane.

Saturday class: 10 AM – Noon, Randell 121.

Week 8.  Matrix transpose. Orthonormal bases. Orthogonal projection onto a subspace.

Orthogonalization of vectorsOrthogonal matrices. Homogeneous equations and orthogonality.

Week 9.  Midterm 2 (3.1-3.4, 5.1-5.3). Determinants. Cramer’s rule.

Week 10. Eigenvalues and eigenvectors. Eigenspaces. Examples. Algebraic and geometric multiplicities.

Quiz 6 (eigenvalues and eigenvectors). Eigenbases and diagonalization. Examples.