Linear Algebra | Master Course Outlines | Academics

MATH260 Linear Algebra

3 credits

2250

MATH140 (C or better)

None

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.

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.
Planned Sequence of Topics and/or Learning Activities
1. Systems of Equations
2. Vector Spaces
3. Geometric Examples
4. Linear Mappings
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.
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.