Math 261 – Linear Algebra, Winter 2011

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Instructor: Anatolii Grinshpan
Office hours:  MT 6-7, Korman 253, or by appointment.

Syllabus    Academic calendar    Math resource center   

Jan 3. Introduction to the course.  Systems of linear equations.

          Elementary row operations.

 

Jan 4. Gaussian elimination. Row echelon form. Pivots, basic and free variables.

          Homework 1: due Tuesday, January 11.

 

Jan 10. Reduced echelon form (Gauss-Jordan elimination). Uniqueness.

            Linear combinations. Span. Vector equations.

 

Jan 11. Vector equations and matrix equations. Homogeneous systems.

            Homework 2: due Tuesday, January 18.

 

Jan 17. MLK day.

 

Jan 18. Homogeneous and inhomogeneous systems. The structure of solutions.

            Linear dependence and linear independence.

            Homework 3: due Tuesday, January 25.

 

Jan 24. Linear dependence and independence. Linear transformations.

             Additional reading: examples of applications.

                                                                            

Jan 25. The range of a linear transformation. The matrix of a linear transformation.

             One-to-one and onto.

             Homework 4: due Monday, January 31.

 

Jan 31. Discussion.

 

Feb 1. Midterm 1 (Chapter 1).

           Homework 5: none.

 

Feb 7. Exam discussion. Operations on matrices.

 

Feb 8. The inverse matrix. Elementary matrices.

           Homework 6: due Tuesday, February 15.

 

Feb 14. Invertible matrices. Examples.

 

Feb 15. Partitioned matrices. Triangular factorizations.

             Homework 7: due Tuesday, February 22.

 

Feb 21. The LU decomposition.

 

Feb 22. Subspaces. Dimension and rank.

             Homework 8: due Monday, February 28.

 

Feb 28. Discussion.

 

Mar 1. Midterm 2 (Chapter 2).

            Homework 9: none.

 

Mar 7. Exam discussion. Determinants.

 

Mar 8. Determinants. Cramer’s rule.

            Homework 10: due Monday, March 14.

 

Mar 14. Introduction to Matlab (Korman C-104).

 

Mar 15. Final Exam (Chapters 1-3, Section 4.1).