Linear Algebra – mth530 (3 credits)
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.
- Apply kernel and range to linear transformations.
- Define linear transformations, the geometry of linear operators, and the invertibility of linear transformations.
- Describe matrices as transformations.
General Vector Spaces
- Define vector spaces and subspaces.
- Analyze the relationship of linear independence and vector spaces.
Systems of Linear Equations
- Apply linear systems.
- Explain systems of linear equations.
- Solve linear systems by row reduction.
Matrices and Matrix Algebra
- Describe operations on matrices.
- Demonstrate inverses of matrices.
- Perform matrix factorizations.
- Explain geometry and algebra of vectors.
- Identify dot products.
- Describe vector equations of lines and planes.
- Explain the properties of determinants.
- Apply Cramer’s rule in calculating determinants.
- Identify eigenvalues and eigenvectors.
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