MATH 251 - Introduction to Linear Algebra
Credit Hours: 3
Billable Contact Hours: 3
Prerequisites: A grade of C or better in MATH 171 , Calculus I, within the last three years is highly recommended
MTA Mathematics Satisfier Y
Session Cycle: WI
Matrix operations, echelon form, solutions of systems of linear equations, basics of vector spaces, subspaces, and linear transformations: span, linear independence, bases, dimension, matrix representation of linear transformations; determinants; characteristic polynomials, eigenvalues, eigenvectors, Jordan canonical form, inner-product spaces (including orthogonal polynomials); unitary, self-adjoint, and orthogonal matrices, least squares method, discrete Markov processes; bilinear and quadratic forms; introduction to the spectral theorem. Students will be expected to work with mathematics numerically, graphically, analytically, and verbally.
Notes: Science/Mathematics Division
Theory Hours: 45
Learning Outcomes: 1. Solve a system of linear equations by row reduction, Cramer’s rule, and using an inverse matrix.
2. Compute eigenvalues and eigenvectors of a matrix and write it in Jordan canonical form and its spectral decomposition.
3. Apply the least squares method to fit data to polynomials.
4. Analyze discrete Markov processes.
5. Use an appropriate inner product to find a polynomial approximation to a continuous function.
6. Geometrically interpret and construct a matrix for a linear transformation.
7. Demonstrate understanding of basis, span, dimension, linear independence, linear dependence, and the Gram-Schmidt process.
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