ࡱ> DFCa bjbj <5AbAbt t 8<,hD)*0)))))))$Y+.)))+!+!+!)+!)+!+!V'@(@aM~9( ))0)*(x.8.(.(+!)))*.t B :  GROSSMONT COLLEGE Official Course Outline MATHEMATICS 284 LINEAR ALGEBRA 1. Course Number Course Title Semester Units Semester Hours MATH 284 Linear Algebra 3 3 hours lecture: 48-54 hours 96-108 outside-of-class hours 144-162 total hours 2. Course Prerequisites A C grade or higher or Pass in MATH 280 or equivalent. Corequisite None Recommended Preparation None. 3. Catalog Description This course develops the techniques and theory needed to solve and classify systems of linear equations. Solution techniques include row operations, Gaussian elimination, and matrix algebra. Investigates the properties of vectors in two and three dimensions, leading to the notion of an abstract vector space. Vector space and matrix theory are presented including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Selected applications of linear algebra are included. 4. Course Objectives The student will: Find solutions of systems of equations using various methods appropriate to lower division linear algebra. Use bases and orthonormal bases to solve problems in linear algebra. Find the dimension of spaces such as those associated with matrices and linear transformations. Find eigenvalues and eigenvectors and use them in applications. Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues. 5. Instructional Facilities Standard classroom equipped with: a. Whiteboards b. Overhead projector/document camera c. SmartCart 6. Special Materials Required of Student Graphing calculator. MATHEMATICS 284 LINEAR ALGEBRA page 2 7. Course Content Techniques for solving systems of linear equations including Gaussian and Gauss-Jordan elimination and inverse matrices. Matrix algebra, invertibility, and the transpose. Relationship between coefficient matrix invertibility and solutions to a system of linear equations and the inverse matrices. Special matrices: diagonal, triangular, and symmetric. Determinants and their properties. Vector algebra for Rn. Real vector space and subspaces. Linear independence and dependence. Basis and dimension of a vector space. Matrix-generated spaces: row space, column space, null space, rank, nullity. Change of basis. Linear transformations, kernel and range, and inverse linear transformations. Matrices of general linear transformations. Eigenvalues, eigenvectors, eigenspace. Diagonalization including orthogonal diagonalization of symmetric matrices. Inner products on a real vector space. Dot product, norm of a vector, angle between vectors, orthogonality of two vectors in Rn. Angle and orthogonality in inner product spaces. Orthogonal and orthonormal bases: Gram-Schmidt process. 8. Method of Instruction The development of problem-solving techniques may be achieved by using a variety of instructional techniques including instructor presented lecture and examples, individual and group work, and daily problem assignments. 9. Methods of Evaluating Student Performance a. Homework b. Quizzes c. Tests b. In-class comprehensive final exam. 10. Outside Class Assignments a. Homework/Problem sets. b. Take-home tests. 11. Texts a. Required Text(s) selected from: (1) Anton, Howard. Elementary Linear Algebra. New York, NY: John Wiley & Sons, 10th ed 2010 . (2) Poole, David. Linear Algebra, A Modern Introduction. Boston, MA: Brookes/Cole , 2011, 3rd ed. b. Supplementary texts and workbooks: None. MATHEMATICS 284 LINEAR ALGEBRA page 3 Addendum: Student Learning Outcomes Upon completion of this course, our students will be able to do the following: Characterize and solve a system of linear equations, and determine types of solutions and the existence of a solution. Classify matrices and their properties. Demonstrate and analyze the use of matrix algebra with its associated properties. Demonstrate and analyze the use of the determinant with its associated properties. Demonstrate and analyze the use of vector spaces, linear transformations, eigenvalues and eigenvectors. Analyze, identify, and use appropriate methods, definitions, and techniques in solving application problems. 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