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Course level: Graduate
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.
This graduate level course requires proof of completion of a Bachelor's degree. Be prepared to provide documentation during the checkout process.
What you'll learn
Course skills and outcomes
Systems and Linear Equations
- Solve systems of linear equations.
- Create spans using vector matrices.
- Apply linear systems to real-world scenarios.
Linear Transformations, Models, and Matrices
- Transform linear matrices.
- Demonstrate matrix operations.
- Create inverse of matrices.
- Examine applications of linear algebra in economics using Leontief’s closed model.
- Apply LU (Lower Upper) factorization to matrices.
- Describe vector spaces and subspaces.
- Determine dimension and rank for matrices.
Determinants, Eigenvalues & Eigenvectors, and General Vector Spaces
- Identify properties of determinants.
- Apply Cramer’s Rule to solve a linear system.
- Describe linear transformations using kernel and range.
- Identify eigenvalues and eigenvectors.
Vectors, Dot Products, and Markov Chains
- Model linear equations using coordinate vectors.
- Perform change of basis on a matrix.
- Apply Markov chains to real-world problems.
- Calculate orthogonal vectors using dot product.
Review Topics and Objectives from All Weeks
- Apply the concepts presented in this course.