***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Text: “Introduction to Linear Algebra” " by Gilbert Strang, Fourth Edition. Wellesley-Cambridge Press.

Text Web Site: http://web.mit.edu/18.06/www/

Online Lectures: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

Prerequisite: Credit for or concurrent enrollment in MATH 1432.
Course Description: Solutions of linear systems of equations, vector spaces and subspaces, orthogonality, determinants, linear transformations.

Course Outline

Chapter 1: Introduction to Vectors

1.1-1.2 Vectors and Linear Combinations, Lengths and Dot Products

Chapter 2: Solving Linear Equations

2.1 Vectors and Linear Equations
2.2 The Idea of Elimination
2.3 Elimination Using Matrices.
2.4 Rules for Matrix Operations
2.5 Inverse Matrices
2.6 Elimination = Factorization: A = LU
2.7 Transposes and Permutations
Exam

Chapter 3:  Vector Spaces and Subspaces

3.1 Spaces of vectors
3.2 The Nullspace of A: Solving Ax = 0
3.3 The Rank and the Row Reduced Form
3.4 The Complete Solution to Ax = b.
3.5 Independence, Basis and Dimension
3.6 Dimensions of the Four Subspaces

Chapter 4: Orthogonality

4.1 Orthogonality of the Four Subspaces
4.2 Projections
4.3* Least Squares Approximations (Optional)
4.4 Orthogonal Bases and Gram-Schmidt
*Application to least squares at end of 4.4 is optional
 
Exam

Chapter 5: Determinants

5.1 The Properties of Determinants
5.2 Permutations and Cofactors
5.3 Cramer’s Rule, Inverses, and Volumes

Chapter 6: Eigenvalues and Eigenvectors

6.1 Introduction to Eigenvalues
6.2 Diagonalizing a Matrix
6.4 Symmetric Matrices
6.5 Positive Definite Matrices
6.6 Similar Matrices
6.7* Singular Value Decomposition (Optional)
Exam

Chapter 7: Linear Transformations

7.1 The Idea of a Linear Transformation
7.2 The Matrix of a Linear Transformation
Review

Final Exam