# 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
1. ### Course Learning Goals

Students will:

1. solve a system of linear equations;
2. reduce a matrix to reduced echelon form;
3. solve a matrix equation;
4. recognize a vector space, subspace;
5. determine a basis for a vector space and the dimension of a vector space;
6. determine coordinates for a vector relative to a given basis;
7. perform dot product and apply to defining norm and orthogonality;
8. recognize a linear mapping;
9. determine domain, null space, and range for a given linear mapping and relate the dimensions of these three vector spaces;
10. find a matrix for a linear mapping;
11. perform matrix products (composition of mappings);
12. find an inverse of a nonsingular matrix (inverse of a mapping);
13. apply matrix algebra to Leontief model, population model;
14. evaluate determinant and relate to theory;
15. recognize similar matrices;
16. determine eigenvalues and eigenvectors;
17. determine diganonability; and
18. apply theory of eigenvalues to Markov model.
2. ### Planned Sequence of Topics and/or Learning Activities

1. Systems of Equations
1. Solutions using matrices
2. Row reduction
3. Existence and uniqueness of solutions
4. Set of solutions as an example of a vector space
5. Matrices
6. Matrix equations
2. Vector Spaces
1. Definitions
2. Examples: Rn, C[0,1]
3. Subspaces
4. Independence and spanning
5. Bases and coordinates
3. Geometric Examples
1. R2 and R3
2. Dot product
3. Norm
4. Orthogonality
4. Linear Mappings
1. Homomorphisms, isomorphisms
2. Null space of mapping
3. Linear mappings
4. Composition of mappings
5. Product of matrices
6. Inverse of a mapping
7. Inverse of a matrix
8. Algebra of matrices
9. Determinants
10. Leontief models
11. Similar matrices
12. Eigen vectors and values
13. Diagonability
14. Invariant subspaces
15. Markov chains
16. Quadratic forms - optional
3. ### 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.
4. ### Reference, Resource, or Learning Materials to be used by Student:

Departmentally-selected textbook. Details provided by the instructor of each course section. See course syllabus.

Review/Approval Date - 4/06; New Core 8/2015