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.
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.
Quiz 5 (linear independence). Coordinates. Matrix with respect to a given basis.
Saturday class: 10 AM – Noon, Randell 121. Lecture notes.
Week 8. Matrix transpose. Orthonormal bases. Orthogonal projection onto a subspace.
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.
March 20. Questions session: 10 AM-Noon, Pearl 303.
Office hours: 1-3PM, Korman 207.
March 21. Final exam: 10:30-12:30, Stratton 113. (answer key)