Pennsylvania State University Spring Semester 2011 MATH 220 Matrices Course Information Last updated February 11 2011 The Latest Version of This Document This document is subject to revision during the semester The latest version of this document is available on line at http www math psu edu simpson courses math220 Course Description Systems of linear equations matrix algebra eigenvalues and eigenvectors orthogonality and least squares symmetric matrices and quadratic forms Prerequisite MATH 110 or MATH 140 Textbook Linear Algebra and its Applications Updated Third Edition by David Lay published by Pearson Addison Wesley Calculators The use of calculators will not be permitted on exams Calculators may be used but are not required on homework assignments Midterm Exam A 75 minute evening exam will be held on Tuesday March 1 2011 from 6 30 to 7 45 PM Conflict and Makeup Midterm Exams Only students with official University conflicts will be allowed to schedule the conflict midterm exam Only students with a valid documented excuse will be permitted to schedule the makeup exam with no penalty Students without a valid documented excuse may be allowed to take a makeup exam but they will receive a mandatory 20 point deduction on their scores 1 The conflict midterm exam will be 5 05 PM to 6 20 PM on Tuesday March 1 2011 Students taking the conflict exam will not be allowed to leave the examination room until 6 25 PM Any student who leaves the room before 6 25 PM will receive a score of zero on the exam and will not be allowed to retake it You must sign up for the conflict exam in class with your instructor on a pink form You are responsible for knowing the room and time of the conflict exam This information is on the top of the pink form Note that your instructor must turn in the pink form 48 hours prior to the examination date If you have not signed up with your instructor you will not be allowed to take the conflict exam For the makeup exam you must sign up with your instructor on a yellow form as soon as possible following the regular exam date Final Exam A comprehensive final exam covering the entire content of the course will be given The final exam period is Monday May 2 through Friday May 6 Students must not plan to leave University Park before Saturday May 7 Conflict and Makeup Final Exams For the final exam notification of conflicts is given on the student s final exam schedule on e Lion A student must take action to request a conflict exam through e Lion during the period February 14 through March 6 2011 Note that the conflict final exam is scheduled by the Registrar s office not by the Department of Mathematics Students who miss both the regular and the conflict final exams due to a valid and documented reason such as illness may be allowed to take a makeup final exam If a student does not have a valid reason a 30 point penalty will be imposed All such makeup exams must be scheduled through the instructor and students must contact the instructor within 24 hours of the final exam Grading Policy Grades will be assigned on the basis of 350 points distributed as follows 100 points for homework and quizzes 100 points for the midterm exam 150 points for the final exam Final grades will be assigned as follows A 325 350 A 315 324 B 304 314 B 290 303 B 280 289 C 269 279 C 245 268 D 210 244 F 0 209 Note that we do not use a curve in this course Grades will be based exclusively on homework quizzes the midterm exam and the final exam There is no extra credit work for this course 2 Math Center and Tutors Free mathematics tutoring is available at Penn State Learning http www PennStateLearning psu edu located in 7 Sparks Building If you need additional help you may consult the list of private tutors maintained by the undergraduate office Students are expected to pay for their tutoring session The Private Tutor List is available through the home page of the Undergraduate Program of the Department of Mathematics at http www math psu edu ug This web site is also a good source of general information about undergraduate mathematics courses evening exam schedules office hours of instructors etc Academic Integrity All Penn State and Eberly College of Science policies regarding academic integrity apply to this course For details see http www science psu edu academic Integrity Questions Problems Comments If you have questions or concerns about a grade or course related issue regarding MATH 220 please consult your instructor first If this does not result in a satisfactory solution please consult the course coordinator Stephen G Simpson simpson math psu edu If you still cannot resolve the problem please consult the Associate Head For Undergraduate Studies James Sellers sellersj math psu edu Course Outline tentative subject to revision Sections of the textbook are indicated Dates and number of class periods are in parentheses I LINEAR EQUATIONS IN LINEAR ALGEBRA 1 1 1 2 1 3 1 4 1 5 1 7 1 8 1 9 Systems of Linear Equations 1 5 January 11 13 Row Reduction and Echelon Forms 1 5 January 13 18 Vector Equations 1 5 January 20 25 The Matrix Equation Ax b 1 January 25 27 Solution Sets of Linear Systems 1 January 27 February 1 Linear independence 1 February 1 3 Introduction to Linear Transformations 1 February 3 8 The Matrix of a Linear Transformation 1 February 8 10 continued on next page 3 II MATRIX ALGEBRA 2 1 2 2 2 3 2 8 Matrix Operations 1 February 10 15 The Inverse of a Matrix 1 February 15 17 Characterizations of Invertible Matrices 1 February 17 22 Linear Subspaces 1 5 February 22 24 REVIEW FOR MIDTERM EXAM March 1 MIDTERM EXAM March 1 2 9 Dimension and Rank 1 5 March 3 15 III DETERMINANTS 3 1 Introduction to Determinants 1 March 15 17 3 2 Properties of Determinants 1 March 17 22 IV EIGENPROBLEMS 5 1 Eigenvalues and Eigenvectors 2 March 22 24 29 5 2 The Characteristic Equation 1 March 29 31 5 3 Diagonalization 1 March 31 April 5 V ORTHOGONALITY AND LEAST SQUARES 6 1 6 2 6 3 6 4 6 5 Inner Product Length and Orthogonality 0 5 April 5 Orthogonal Sets 1 April 7 Orthogonal Projections 1 April 12 The Gram Schmidt Process no QR Factorization 1 April 14 Least Squares Problems Example 1 from 6 6 1 April 19 VI SYMMETRIC MATRICES 7 1 Diagonalization of Symmetric matrices Spectral Theorem 1 April 21 7 2 Quadratic Forms 1 April 26 REVIEW FOR FINAL EXAM April 28 FINAL EXAM Final Exam Week May 2 6 4