An examination of systems of linear equations and matrices, elementary vector-space concepts and geometric interpretations. Discusses finite dimensional vector spaces, linear functions and their matrix representations, determinants, similarity of matrices, inner product, rank, eigenvalues and eigenvectors, canonical form and Gram-Schmidt process. Computer software will demonstrate computational techniques with larger matrices. Graphing calculator or appropriate software may be required.
- Demonstrate proficiency in correct formulation and solving linear problems in terms of systems of linear equations in matrix notation.
- Have a strong knowledge of mathematical vocabulary and notation of matrix algebra.
- Have a clear understanding of the concepts of vector spaces and linear transformations.
- Show ability to work with inner products and orthogonal matrices, to solve eigenvalue problems.
- Know how to apply the linear algebra techniques to handle linear mathematical models (solving systems of linear differential equations, least squares fitting to data problems, etc.).
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