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MATH260 Linear Algebra
Department of Science, Technology, Engineering & Mathematics: Mathematics
- I. Course Number and Title
- MATH260 Linear Algebra
- II. Number of Credits
- 3 credits
- III. Number of Instructional Minutes
- 2250
- IV. Prerequisites
- MATH140 (C or better)
- Corequisites
- None
- V. Other Pertinent Information
- None
- VI. Catalog Course Description
- Topics for this course include: vector spaces, linear transformations, matrix algebra, change of bases, similarity, diagonalization, eigenvalues and vectors; with application to solutions of systems of linear equations, linear programming, Leontief models, Markov chains, codes, and quadratic forms.
- VII. Required Course Content and Direction
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Course Learning Goals
Students will:
- solve a system of linear equations;
- reduce a matrix to reduced echelon form;
- solve a matrix equation;
- recognize a vector space, subspace;
- determine a basis for a vector space and the dimension of a vector space;
- determine coordinates for a vector relative to a given basis;
- perform dot product and apply to defining norm and orthogonality;
- recognize a linear mapping;
- determine domain, null space, and range for a given linear mapping and relate the dimensions of these three vector spaces;
- find a matrix for a linear mapping;
- perform matrix products (composition of mappings);
- find an inverse of a nonsingular matrix (inverse of a mapping);
- apply matrix algebra to Leontief model, population model;
- evaluate determinant and relate to theory;
- recognize similar matrices;
- determine eigenvalues and eigenvectors;
- determine diganonability; and
- apply theory of eigenvalues to Markov model.
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Planned Sequence of Topics and/or Learning Activities
- Systems of Equations
- Solutions using matrices
- Row reduction
- Existence and uniqueness of solutions
- Set of solutions as an example of a vector space
- Matrices
- Matrix equations
- Vector Spaces
- Definitions
- Examples: Rn, C[0,1]
- Subspaces
- Independence and spanning
- Bases and coordinates
- Geometric Examples
- R2 and R3
- Dot product
- Norm
- Orthogonality
- Linear Mappings
- Homomorphisms, isomorphisms
- Null space of mapping
- Linear mappings
- Composition of mappings
- Product of matrices
- Inverse of a mapping
- Inverse of a matrix
- Algebra of matrices
- Determinants
- Leontief models
- Similar matrices
- Eigen vectors and values
- Diagonability
- Invariant subspaces
- Markov chains
- Quadratic forms - optional
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Assessment Methods for Course Learning Goals
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.
A minimum of 70% of a student's grade must be determined from proctored assessments and work. These proctored assessments include tests, quizzes, or other proctored in-class assignments.
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Reference, Resource, or Learning Materials to be used by Student:
Departmentally-selected textbook and TI-83/84 calculator. Details provided by the instructor of each course section. See course syllabus.
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Review/Approval Date - 4/06; New Core 8/2015; Updated 11/2019