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# MATH 220 - Linear Algebra

5 Credits
Introduction to Linear Algebra: Row operation, matrix algebra; vector spaces, orthogonality, Gram-Schmidt orthogonalization, projections, linear transformations and their matrix representations, rank, similarity; determinants; eigenvalues, eigenvectors, and least squares.

Pre-requisite(s) MATH& 152 min 2.0
Course Note Math& 153 recommended.
Fees

Quarters Typically Offered

Winter Day
Spring Day

Designed to Serve Transfer students in mathematics, engineering, and the sciences
Active Date 2014-04-25

Class Limit 32
Contact Hours: Lecture 55 Lab 0 Field Studies 0 Clinical 0 Independent Studies 0
Total Contact Hours 55
Degree Distributions:
AA
• Quantitative Skills
• Science

ProfTech Related Instruction
• Computation

PLA Eligible Yes

Course Outline
• Gaussian elimination, matrix algebra, elementary matrices.
• Vector spaces, geometric vectors, subspaces, bases, linear independence/dependence, dimension.
• Vector product spaces, orthogonality, Gram-Schmidt process, orthogonal projections.
• Linear transformations and their matrix representations, change of basis, similarity.
• Properties of determinants, eigenvalues, eigenvectors, eigenspaces.
• Applications; data fitting, least squares.
• Emphasis: Mathematical proof (reading, understanding, and writing).

Student Learning Outcomes
Solve systems using Gauss-Jordan elimination.

Identify and orthogonalize the basis of a vector space.

Apply matrix methods to model a data set using least squares regression.

Calculate and interpret the eigenvalues and eigenvectors of a matrix.

Identify, create, and apply linear transformations using matrix methods.

Construct a mathematical proof.