# Math 201 – Linear Algebra, Winter 2013

Instructor: Anatolii Grinshpan
Office hours:  TR 12 – 1, Korman 247, or by appointment, Korman 253.

Course information   Schedule   Academic Calendar       Some links: Terrell, Strang, Tutoring center

Jan. 7. Introduction to the course. Systems of linear equations. Elementary row operations.

Jan. 9. Gaussian elimination algorithm. Echelon form of a matrix. Leading and free variables. Solutions of a linear system.

Reading: 1.1, 1.2, 1.3. Problems.

Jan. 14. The rank of a matrix. The number of equations and unknowns versus the number of solutions. Matrix algebra.

Jan. 16. Quiz 1 (Gaussian elimination). Dot product. Linear combinations of vectors. Matrix-vector product.

Reading: 1.3. Problems.

Jan. 21. No class (MLK day).

Jan. 23. Quiz 2 (matrix-vector product). Linear transformations.

Reading: 2.1. Problems.

Jan. 28. The matrix of a linear transformation. Linear transformations and geometry: examples.

Jan. 30. Quiz 3 (linear transformations of the plane). Matrix product.

Reading: 2.2, 2.3. Problems.

Feb. 1. Questions sessions: 12 – 1 and 6 – 7, Randell 121.

Feb. 4. Midterm 1 (1.1-1.3, 2.1-2.3).

Feb. 6. Matrix product. Multiplication by elementary matrices. Block multiplication. The inverse matrix.

Reading: 2.3, 2.4. Problems.

Feb. 11. Quiz 4 (matrix inversion). 2x2 inversion. Example. Example. Image and kernel of a linear transformation.

Feb. 13. Image and kernel. Span. Characterizations of invertibility. Linear dependence and independence.

Reading: 3.1, 3.2. Problems.

Feb. 18. Quiz 5 (image and kernel). Subspaces. Basis and dimension of a subspace.

Feb. 20. Subspaces associated to a matrix. Basis for the kernel. Basis for the image. Rank-nullity theorem.

Reading: 3.2, 3.3. Problems.

Feb. 25. Coordinates relative to a given basis.

Reading: 3.4. Problems.

Feb.25. Questions session: 6 – 7+, PISB 108.

Feb. 27. Midterm 2 (2.4, 3.1-3.4).

Mar. 4. The transpose of a matrix. Permutation matrices. The determinant of a matrix.

Reading: 6.1. Problems: 1-22 (page 275)

Mar. 6. Quiz 6 (determinants). Example. Laplace expansion. Multiplicativity of the determinant.

Reading: 6.2. Problems: 1, 3, 5, 7, 9, 28, 29, 30, 35.

Mar. 11. Cramer’s rule (pages 300-305). Diagonalizable matrices. Eigenvalues and eigenvectors.

Reading: 7.1. Problems: 22-24 (page 307), 1-10, 15, 16, 18, 19 (pages 323-324).

Mar. 13. Quiz 7 (eigenvalues and eigenvectors). Eigenspaces. Diagonalization theorem. Examples.

Reading: 7.2, 7.3. Problems: 1-13, 15, 17-19, 22, 24 (page 336);  1-19 (odds), 21-28 (page 345).

Mar. 18. Examples and questions.

Practice questions: Set 1 Set 2 Set 3 Set 4 Set 5 Set 6

Mar. 21. Final exam (all lectures): 10:30-12:30, CAT 61.