# Math 201 – Linear Algebra, Spring 2015

Instructor: Anatolii Grinshpan
Office hours:  Mon 2-3 & Wed 1-3,  Korman 249.

Mar 31. Introduction to the course. Gauss-Jordan elimination.

Apr 2.   Reduced echelon form. Leading and free variables. Rank. Example.

Reading: 1.1, 1.2. Problems

Apr 7. Quiz 1 (Gaussian elimination). Tall, long, square. The structure of solutions. Vectors.

Apr 9. Linear combinations of vectors. Matrix-vector product and its properties.

Apr 14. Quiz 2 (matrix-vector product). Linear transformations. The matrix of a transformation.

Apr 16. Projections, reflections, rotations and their matrices. Inversion. Matrix product.

Reading: 2.1, 2.2. Problems Problems

Apr 21. Properties of matrix multiplication. Reading: 2.3. Problems

Apr 23. Midterm 1 (lectures of March 31 - April 21).

Apr 28. Invertible transformations. Matrix inversion. Inverses of elementary matrices. Reading: 2.4. Problems

Apr 30. Quiz 3 (matrix inversion). Transpose. Block multiplication and inversion. Image of a linear transformation. Span.

May 5. Kernel of a linear transformation. Subspaces. Linear independence. Reading: 3.1, 3.2. Problems Problems

May 7. Quiz 4 (image and kernel). Vector relations. Basis and dimension. Basis for the kernel. Basis for the image. Rank-nullity theorem.

Subspaces associated to a matrix. Reading: 3.3. Problems

May 12. Characterizations of linear independence. Characterizations of invertibility. Coordinates relative to a given basis.

May 14. Quiz 5 (basis and dimension). The matrix of a linear transformation relative to a given basis.

May 19. Orthogonal projections and orthonormal bases. Reading: 5.1. Problems

May 21. Midterm 2 (lectures of April 28 - May 19).

May 26. Matrix of the orthogonal projection. Orthogonal transformations and matrices. Determinants. Reading: 5.3. Problems

May 28. Properties of the determinant. Reading: 6.1, 6.2. Problems (answers). Eigenvalues and eigenvectors.

June  2. Quiz 6 (determinants). Eigenspaces and eigenbases. Examples. Reading: 7.1-7.3. Problems

June  4. Cross-product transformation. Diagonalization. Symmetric matrices.

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

June 11. Questions session: 10-Noon, Stratton 101. Example.

June 12. Final exam: 10:30-12:30 AM, Lebow 241.