Math 201 – Linear Algebra, Fall 2015

      

Instructor: Anatolii Grinshpan
Office hours:  TWR 3-4,  Korman 249.

Course information    Academic calendar    Tutoring center 

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

              Reduced echelon form. Rank. Example.

              Reading: 1.1, 1.2. Problems.

 

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).

              Reading: 1.3. Problems.

 

Week 4. Linear transformations, Projections, reflections, rotations and their matrices.

              The matrix of a linear transformation. Orthogonal projection.

              Reading: 2.1, 2.2. Problems. Problems.

 

Week 5. Questions session: Oct 19, 5-6:30PM, Curtis 457. Midterm 1 (weeks 1-4).

              Properties of matrix multiplication. Elementary matrices. Invertible transformations.

              Reading: 2.3. Problems.

 

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

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

              Reading: 2.4. Problems.

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.

              Reading: 3.1. Problems. Reading: 3.2 Problems.

 

Week 8. Quiz 5 (linear independence). Rank-nullity theorem. Coordinates.

              Matrix of a linear transformation with respect to a given basis.

              Reading: 3.3, 3.4. Problems. Problems.

 

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.

                Reading: 7.1-7.3. Problems. Problems. Problems.

 

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.