# Math 201 – Linear Algebra, Fall 2013

Instructor: Anatolii Grinshpan
Office hours:  MTR  2 – 3, Korman 249, or by appointment, Korman 253.

Week 1. Introduction to the course. Systems of linear equations. Elementary row operations.

Gaussian elimination. Reduced echelon form. The rank of a matrix. Leading and free variables.

Week 2. The number of equations and unknowns versus the number of solutions. Matrix-vector product.

Homework discussion. Quiz 1 (1.1, 1.2).

Week 3. Linear combinations of vectors. Linear transformations: first examples.

Homework discussion. Quiz 2 (1.3). The matrix of a linear transformation.

Week 4. Linear transformations and geometry.  Midterm 1 (1.1 - 2.2).

Week 5.  Matrix product. Multiplication by elementary matrices. The inverse matrix. Inversion of 2x2 matrices.

Week 6. Block multiplication and block inversion. The kernel and image of a linear transformation.

Quiz 3 (2.3, 2.4). Span. Characterizations of invertibility.

Week 7. Linear dependence and independence. Subspaces of the Euclidean space.

Quiz 4 (3.1, 3.2). Basis and dimension. Subspaces associated to a matrix. Basis for the kernel.

Week 8. Basis for the image. Rank-nullity theorem. Coordinates.

Quiz 5 (3.3, 3.4). The matrix of a transformation relative to a given basis.

Week 9. Midterm 2 (2.3 -3.4). The transpose of a matrix. Orthogonality. Orthonormal bases.

Orthogonal projections. Orthogonal transformations and orthogonal matrices.

Week 10. The determinant of a matrix.  Permutation matrices.

Week 11. Eigenvalues and eigenvectors. Example.  Eigenspaces and eigenbases. Examples.

Dec 9. Questions session: 10:30-12:20, Lebow 135.

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

Dec 11. Final exam (all lectures): 1-3 PM, Disque 108.