Linear Algebra
Course Description
The purpose of this course is to provide an introduction to linear algebra, a branch of mathematics dealing with matrices and vector spaces. This course describes the use of linear algebra as a compilation of diverse, but interrelated ideas that provide a way of analyzing and solving problems in many applied fields. Linear algebra has three sides: computational techniques, concepts, and applications. One of the goals of this course is to help you master all facets of the subject and see the interplay among them. The material presented in this course involves theorems, proofs, formulas, and computations of various kinds.
Topics and Objectives
Vectors
- Explain geometry and algebra of vectors
- Identify dot products
- Describe vector equations of lines and planes
Systems of Linear Equations
- Explain systems of linear equations
- Solve linear systems by row reduction
- Apply linear systems
Matrices and Matrix Algebra
- Describe operations on matrices
- Demonstrate inverses of matrices
- Perform matrix factorizations
Determinants
- Explain the properties of determinants
- Apply Cramer's rule in calculating determinants
- Identify eigenvalues and eigenvectors
Linear Transformations
- Define linear transformations, the geometry of linear operators, and the invertibility of linear transformations
- Describe matrices as transformations
- Apply kernel and range to linear transformations
General Vector Spaces
- Define vector spaces and subspaces
- Analyze the relationship of linear independence and vector spaces