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.
Reading: 1.3. Problems
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.
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 7. Quiz 4 (image and kernel). Vector relations. Basis and dimension. Basis for the kernel. Basis for the image. Rank-nullity theorem.
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.
Reading: 3.4. Problems
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
June 11. Questions session: 10-Noon, Stratton 101. Example.
June 12. Final exam: 10:30-12:30 AM, Lebow 241.