MATH 215 LINEAR ALGEBRA ASSIGNMENT SHEET odd, 14, 25, 27, 29, 37, 41, 45, 47, 49, 51, 55, 61, 63, 65, 67, 77, 79, 81

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1 MATH 215 LINEAR ALGEBRA ASSIGNMENT SHEET TEXTBOOK: Elementary Linear Algebra, 7 th Edition, by Ron Larson 2013, Brooks/Cole Cengage Learning ISBN-13: Chapter 1: Systems of Linear Equations odd, 14, 25, 27, 29, 37, 41, 45, 47, 49, 51, 55, 61, 63, 65, 67, 77, 79, odd, 14, 17, 18, odd, all, 45, 53, a, 5a, 17, 19, 29, 31, 33 Chapter 2 Matrices odd, 43, 47, 51, 53, 57, 59, 65, 67, 78, odd, all, 35, 37, 39, 43, 47, 51, 53, 55, 59, 67, , 6, 7, odd, 31, 33, 41, 43, 45, 47, 53, 55, 65, 69, 73, odd, 19, 25, 27, 31, 35, 37, 49, 53, , 3, 5, 11, 15, 19, 27b, 33 Chapter 3 Determinants odd, odd, 39, 41, 45, 51, 53, 61, , 3, 5, 9, 11, 13, 15, 19, 25, 27, 29, 31, 33, 37, , 3, 9, 15, 17, 19, 21, 23, 25, 27, 31, 33, 37, 41, 55, 61, 65, 73, 77, , 3, 9, 17, 25, 39, 41, 43, 51, 55 Chapter 4 Vector Spaces odd, 33, 37, 39, 45, 47, 51, all, odd, 43, odd, odd, 51, 57, 59, 61, all, 9 57 odd, 67, odd, 69, 71, 73

2 Chapter 4 Vector Spaces (continued) odd, 17, 21, 25, 29, 35, 39, 43, 47, , 5, 13, 17, 21, 27, 31 Chapter 5 Inner Product Spaces 5.1 1, 3, 7 15 odd, odd, 41, 45, odd, 71, odd, 21, 27, 29, 33, 35, 39, 43, odd, 67, 71, 73, 79, 85, , 5, 7, 11, 15, 17, 21, 25, 27, 31, 35, 39, , 5, 11, 15, 19, 23, 29, 33 Chapter 6 Linear Transformations odd, 29, 33, 35, 37, 41, 49, 51, 53, 57, 59, 65, 67, odd, odd, 31, 33, odd, odd, 19, 21, 23, odd, 41, 43, 45, 47, , 5, 7, 9, odd Chapter 7 Eigenvalues and Eigenvectors 7.1 1, 5 25 odd, odd, 54, 55, 63, 65, odd, 15, 19, 23, 25, 27, 33, 35, 37, 39, 40, , 3, 7 17 odd, 23, 25, 27, 33, 35, 39, 41, 43, , 23, 27, 29, 33

3 Objectives: 1. Upon successful completion of the course, the student will know or understand: 1. Systems of linear equations and their solution by Gaussian elimination. 2. Matrices and matrix arithmetic; invertible matrices. 3. Definition and properties of the determinant function 4. Evaluation of determinants by row reduction and cofactor expansion 5. Geometry and arithmetic of vectors in 2-space and 3-space. 6. Dot product, cross product and projections 7. Equations of lines and planes in 3-space. 8. Vector algebra of Euclidean n-space. n m 9. Linear transformations from R to R. 10. Real vector spaces. 11. Subspaces. 12. Linear independence. 13. Basis and dimension. 14. Row space, column space and nullspace of a matrix; rank and nullity. 15. Inner products 16. Angle and orthogonality in inner product spaces. 17. Orthonormal bases and the Gram-Schmidt process 18. Eigenvalues and eigenvectors. 19. Diagonalization of matrices 20. General linear transformations; kernel and range 2. Upon successful completion of the course, the student will demonstrate the ability to: 1. Translate freely between systems of linear equations and augmented matrices and apply row operations to solve linear systems by Gaussian (or Gauss-Jordan) elimination. 2. Use the properties of matrix arithmetic and perform matrix calculations, and determine whether or not a given square matrix is invertible and, if it is, calculate the inverse matrix. 3. Recognize and apply the properties of the determinant function. 4. Evaluate determinants by row reduction and cofactor expansion. 5. Demonstrate facility with vector algebra in the plane and space, and use the geometric interpretation of vectors in problem-solving.

4 6. Compute dot products, cross products and projections and apply these operations in geometric problems. 7. Determine equations of lines and planes in 3-space that satisfy prescribed geometric properties. 8. Use the operations of vector algebra in Euclidean n-space. 9. Demonstrate an understanding of the relationship between a linear n m transformation from R to R and its standard matrix and also apply some specific linear transformations (rotations, reflections, projections) in solving problems. 10. Demonstrate familiarity with a variety of real vector spaces and determine whether or not a given set forms a vector space. 11. Determine whether or not a given subset of a vector space forms a subspace. 12. Determine whether or not a given set of vectors is linearly independent. 13. Find bases for vector spaces and determine their dimension. 14. Find bases for the row space, column space and nullspace of a matrix. Students will understand the relationship between rank and nullity. 15. Recognize and use the properties of inner products. 16. Compute angles between vectors and determine orthogonality in inner product spaces. 17. Use orthogonal/orthonormal bases in computing projections and use the Gram-Schmidt process to construct orthogonal/orthonormal bases. 18. Determine the eigenvalues and eigenvectors of a matrix. 19. Use eigenvectors to diagonalize a matrix that has distinct, real eigenvalues. 20. Recognize and manipulate general linear transformations and determine the kernel and range of a linear transformation.

5 MATHEMATICS DEPARTMENT POLICIES Disruptive Behavior: Behavior that is disruptive to the instructor or students is contrary to quality education. Should the instructor determine that an individual student's verbal or nonverbal behavior is hampering another student's ability to understand or concentrate on the class material, the instructor will speak with that student in an effort to rectify the problem behavior. If the behavior continues after this discussion, the instructor will have the disruptive student leave the class. Permission to return to class may be dependent upon assurances that the student has met with some responsible individual about the problem: the mathematics department chairman, a counselor, the Dean of Student Support Services, etc. Cheating and/or Plagiarism: An instructor who has evidence that a student may have cheated or plagiarized an assignment or test should confer with the student. Students may then be asked to present evidence (sources, first draft, notes, etc.) that the work is his own. If the instructor determines that cheating or plagiarism has occurred, he may assign a failing grade to the test, the assignment, or the course, as he sees fit. Access Office The college s Access Office guides, counsels, and assists students with disabilities. If you receive services through the Access office and need special arrangements (seating closer to the front of the class, a note-taker, extended time for testing, or other approved accommodation), please make an appointment with your instructor during the first week of classes to discuss these needs. Any information you share will be held in strict confidence, unless you give the instructor permission to do otherwise. Attendance and Grading Attendance is expected at all class meetings. Each individual instructor determines the grading system for his/her class. Grading scales, methods of grading, make-up policy, and penalties resulting from excessive absences will be discussed early in the semester. Final Exams (Departmental) In the Fall and Spring semesters, a portion of the final examinations given in MTH:020, MTH:030, MTH:140 and MTH:160 may be designed by the Mathematics Department. All MTH 210, 220, 230 Calculus final examinations will be given during the Wednesday of finals week. In the Summer semesters, any culminating experience ( i.e. Final Exam) is given on the last day of that Summer session. Course Repeater Policy Students must file a petition seeking departmental approval before enrolling in the same Meramec mathematics course for the third time. The petition process will involve writing a formal petition and meeting with a math faculty advisor to design a course of action that will improve chances for success.