Welcome to the Fall 2011 MA237 course webpage!

Syllabus

Announcements

The Exam 2 Review will be posted on Tuesday, October 18^th.

The solutions are now posted.

Exam 2 will cover material from Chapter 4 but not Chapter 5.

For matrix operations, you can use Wolfram Alpha, the USA Engineering Equation Solver, or Octave.

Tentative Schedule and Study Problems

Date	Schedule and links	Homework
August 22^nd	Syllabus Introduction to Linear Algebra …native understanding of independence	Read Ch 1: 1.1 – 1.4
August 24^th	Ch 1: N-tuples in R^n	Ch 1: 41acd,42acd,45,46,48
August 26^th	We’ll work on a problem like #1.48. Ch 1.7: Complex Numbers	Ch 1: 66, 70, 72
August 29^th	Quiz on a problem like 1.48. Complex Numbers Continued	Ch 1: 68 (added)
August 31^st	Quiz on Complex Numbers Ch 2: Matrices	Ch 2: 38, 41ab, 47iii, 50
September 2^nd	Quiz on Properties of Matrix Addition Ch 2: Matrix Multiplication	Ch 2: 39, 41cd, 47iv, 54, 56
September 5^th	Labor Day Holiday
September 7^th	Ch 3: Linear Systems Ch 3: Solving Linear Systems: Overview Back Substitution Method	Ch 3: 49, 50, 51, 52, 21 Solving Linear Systems:
September 9^th	Pivoting Method Augmented Matrix Method Handy Definitions	Ch 3: 56a using back substitution and neatly solve 53abc - using back substitution - using pivoting w/o matrices - using augmented matrices
September 12^th	Quiz like 53 Ch 3: Dimension of the Solution	Ch 3: 54 (for these, consider the rank and the dimension of the solution set)
September 14^th	board solution of 56 a Ch 3: Developing Virtuosity (RREF)	Ch 3: 62 – do each one 3 times
September 16^th	Quiz like 62 Ch 3: Parametric Solutions	Ch 3: 24a, 57a
September 19^th	Ch 3: Applications Exam I Review	Practice Exam Solutions
September 21^st	Exam I	No homework.
September 23rd	Review Exam 1 Generalizing Linear Combinations	Ch 4: 4,7,14,83, 84
September 26^th	Homework Solutions (4.14, 4.84) Ch 4: Definition of a Vector Space	Ch 4: 2, 3, 73
September 28^th	Ch 4: Deducing Corollary Properties (Proofs I)	revisit Ch 4: 2, 3, 73 (Solutions so far…)
September 30^th	Quiz on a Proof (Proofs I) Ch 4: Proving that a set is (or isn’t) a vector space (Proofs II) Also see Paul’s notes.	Ch 4: 72, 74
October 3^rd	FALL BREAK	FALL BREAK
October 5^th	Ch 4: Linear Dependence	Read 4.7! Ch 4: 17, 19, 89, 90, 91a, 92
October 7^th	Ch 4: Subspaces and Spans	Ch 4: 13, 14, 24, 25, 26
October 10^th	Ch 4: Finding A Basis Practice Quiz 7	Study page 127 and 128. Ch 4: 30,31,107,108,109,110
October 12^th	Quiz 7 on Finding the Basis of the Span of a Given Set of Vectors Ch 4: Finding a Basis, Continued
October 14^th	Ch 4: Solutions Sets (Homogeneous Systems and the Translation Theorem)	Ch 4: 99, 102, 103
October 17^th	Ch 4: Coordinates, Mini-Review (slns)	Ch 4: 128, 129, 130, 131
October 19^th	Ch 5: General Transformations	Ch 5: 1-5
October 21^st	Ch 5: Linear Transformations	Ch 5: 49,50,51
October 24^th	Exam II Review (solutions)
October 26^th	Exam II	No homework.
October 28^th	Review Exam II (solutions )and Definition of Linear Transformation	Ch 5: 49,50,51 Extra Practice for Quiz: Ch 5: 9, 10, 11
October 31^st	Quiz 8 (Slns) on Whether a Function is Linear Ch 6: Matrix Representation of a Linear Transformation	Ch 6: 1a, 37a, 40, 42a, 45, 62
November 2^nd	Ch 6: Common Linear Transformations (Worksheet)
November 4^th	Ch 6: Common Linear Transformations Continued (Octave Code) to run this, for example type: M=[1 .5; -.5 1] apply_transformation(M)	Ch 6: 7, 39
November 7^th	Quiz 9 on Common Linear Transformations Revisiting Proving a Function is Linear	Ch 5: 49,50,51 Extra Practice for Quiz: Ch 5: 9, 10, 11
November 9^th	Retake Quiz 8 (Slns) on Whether a Function is Linear Ch 5: Kernel and Image of Linear Mappings	Ch 5: 16, 61, 62, 63, 19, 64
November 11^th	Ch 6: Change of Bases	Homework
November 14^th	Ch 6: Application: Matrix Representation of Differential Operators	Ch 6: 8, 43
November 16^th	Ch 8: Determinants Intro, Method of Cofactors	Ch 8: 1, 2, 6, 39, 40ab, 44, 46
November 18^th	Quiz 10: Method of Cofactors Ch 8: Determinants Method of Row Reduction (worksheet)	Ch 8: 40--43 (using row reduction)
November 21^st	Ch 8: Determinants Properties of Determinants
November 23^rd	Thanksgiving	Thanksgiving
November 25^th	Thanksgiving	Thanksgiving
November 28^th	Ch 9: Eigenvalues and Eigenvectors	Ch 9: 45, 46a, 48
November 30^th	Practice Quiz 11
December 2^nd	Quiz 11: Deriving the Characteristic Polynomial and Finding Eigenvectors Ch 9: Diagonalization	Ch 9: 45, 46, 48
December 5^th	(Exam III Review) (Solutions) Exam III (Solutions)
December 7^th	Final Review (Solutions)
December 14^th	Final Exam