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Kent State | MATH 41021
Theory Of Matrices
100 sample documents related to MATH 41021
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Kent State MATH 41021
MATH 4/51021 Homework #2 Due: Wednesday, February 4 Reading: For Mon., February 2: 4.7; Problems 4.174.23 For Wed., February 4: 4.8, 4.9; Problems 4.244.40 Problems to turn in: 1. Show that the following subsets of R3 are subspaces of R3 . (a) W1 = -
Kent State MATH 41021
Math 4/51021 Summary of Spanning and Linear Independence Let S = {v 1 , . . . , v k } be a subset of a vector space V . SPANNING SETS S spans V if and only if for every vector v in V , the equation x1 v 1 + + x k v k = v has at least one solution. -
Kent State MATH 41021
Math 41021 Exam I Review Exam I will be given in class on Wednesday, February 25, 2009. It will cover Chapter 4, Homework #1#4, and material from class through February 16 (Page 33 of the lecture notes). The exam will consist of statements of definit -
Kent State MATH 41021
Math 4/51021 Theory of Matrices Spring 2009 Instructor: Office: Phone: E-mail: Hours: Text: Dr. D. L. White 212 MSB (330)672-9034 white@math.kent.edu 10:00 10:50 AM MWF; 11:00-11:50 AM TR and by appointment Linear Algebra (Schaum\'s Outline), 4th edi -
Kent State MATH 41021
ADMINISTRATIVE POLICY AND PROCEDURES REGARDING STUDENT CHEATING AND PLAGIARISM Condensed Version For complete policy and procedure go to www.kent.edu/policyregister 3342-3-01.8. Cheating and plagiarism constitute fraudulent misrepresentation for whic -
Kent State MATH 41021
FINAL EXAM SCHEDULESPRING 2009 1. The final examination period for day and evening classes is Monday, May 11, 2009 through Friday, May 15, 2009. Weekend classes, including Friday after 5 p.m., will hold exams during the weekend of May 15-17, 2009, at -
Kent State MATH 41021
Math 4/51021 Theory of Matrices Background Material One of the prerequisites for this course is Math 21001, Linear Algebra. Most of the material from Math 21001 will be assumed, with the exception of vector spaces, which we will cover in slightly mor -
Kent State MATH 41021
Math 4/51021 Guidelines for Writing Proofs Writing a mathematical proof is more or less the same as writing any other essay or composition. In writing a proof, you are trying to convince the reader of the truth of a certain statement. This must be do -
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Kent State MATH 41021
Math 4/51021 Review of Echelon Form and Systems of Equations 1. TERMINOLOGY For basic terminology on systems of equations, related matrix equations, and echelon form, see Chapter 3 of the text. In particular, if E is the row-echelon form of the coeff -
Kent State MATH 41021
MATH 4/51021 Illustration of Proof of Cayley-Hamilton Theorem t - 1 -3 1 1 3 -1 1 2 , so that tI - A = -2 t - 1 -2 and A (t) = |tI - A| = t3 - 3t - 42. Let A = 2 -4 1 t+2 4 -1 -2 Let B(t) be the classical adjoint of tI - A (see 8.9), so B(t) i -
Kent State MATH 41021
Math 4/51021 Some Basic Results on Polynomials For the following results, all polynomials have coefficients from a field K. 1. The greatest common divisor of polynomials f (t) and g(t) is the monic polynomial of highest degree that is a factor of bot -
Kent State MATH 41021
Math 4/51021 Jordan Canonical Form Theorem: Let T : V V be a linear operator with characteristic polynomial T (t) = (t - 1 )n1 (t - 2 )n2 (t - r )nr and minimal polynomial mT (t) = (t - 1 )1 (t - 2 )2 (t - r )r where the i are distinct eigenva -
Kent State MATH 41021
MATH 4/51021 Homework #1 Due: Wednesday, January 28 Reading: For Fri., January 23: 4.1, 4.2, 4.3; Problems 4.14.3 For Mon., January 26: 4.5; Problems 4.84.12 For Wed., January 28: 4.4, 4.6; Problems 4.44.7, 4.134.16 Problems to turn in: Text: 4.71, -
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Kent State MATH 41021
MATH 4/51021 Homework #3 Due: Friday, February 13 Reading: For Mon., February 9: 4.9; Problems 4.414.49 For Wed., February 11: 4.9; Problems 4.504.52 For Fri., February 13: 4.10; Problems 4.534.60 Problems to turn in: Text: 4.89(a), 4.90(a), 4.94. 1 -
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Kent State MATH 41021
MATH 4/51021 Homework #4 Due: Friday, February 20 Reading: For Mon., February 16: 4.11; Problems 4.614.65 For Wed., February 18: 7.1, 7.2, 7.3; Problems 7.17.6 For Fri., February 20: 7.4, 7.5; Problems 7.77.11 Problems to turn in: Text: 4.98, 4.99(a -
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Kent State MATH 41021
MATH 4/51021 Homework #5 Due: Monday, March 2 Reading: For Fri., February 27: 7.6 (up to Projections); Problems 7.127.18 For Mon., March 2: 7.6 (Projections), 7.7; Problems 7.197.31 (especially 7.14, 7.18) Problems to turn in: 1. Let u = (1, 1, 1, 1 -
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Kent State MATH 41021
MATH 4/51021 Homework #6 Due: Friday, March 6 Reading: For Weds., March 4: 5.1, 5.2, 5.3; Problems 5.15.15 For Fri., March 6: 5.4; Problems 5.165.23 Problems to turn in: Text: 7.68, 7.69, 7.72, 7.74(b,c,d), 7.75, 7.76(a) 1. Let V be the vector space -
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Kent State MATH 41021
MATH 4/51021 Homework #7 Due: Friday, March 13 Reading: For Mon., March 9: 5.5, 5.6, 5.7; Problems 5.245.33, 5.38 For Weds., March 11: 6.1, 6.2, 6.5; Problems 6.16.12, 6.316.35 For Fri., March 13: 6.3, 6.4; Problems 6.136.26 Problems to turn in: Tex -
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Kent State MATH 41021
MATH 4/51021 Homework #8 Due: Friday, March 20 Reading: For Weds., March 18: Review Ch. 8 [see notes Problems 9.19.8 For Mon., March 30: 9.4, 9.5; Problems 9.99.11, 9.139.23 Problems to turn in: 1. Show that if the linear tra -
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Kent State MATH 41021
MATH 4/51021 Homework #9 Due: Friday, April 10 Reading: For Fri., April 10: 9.7, 9.8; Problems 9.279.37 Problems to turn in: 1. Find the characteristic polynomial A (t) for the matrix 1 2 1 A = 2 1 -2 . -3 2 -1 2. Find the characteristic polynom -
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Kent State MATH 41021
MATH 4/51021 Homework #10 Due: Friday, April 17 Reading: For Wed., April 15: 10.1, 10.2, 10.3; Problems 10.110.6 For Mon., April 20: 10.4; Problems 10.7, 10.8 Problems to turn in: Text: 9.45(a,b), 9.46, 9.48(b), 9.48(c), 9.61(a), 9.62(a,b), 9.63, 9.6 -
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Kent State MATH 41021
MATH 4/51021 Homework #10 Notes For an n n matrix A, we define the linear operator A on Rn by A (v) = Av. Therefore, all eigenvectors of A must be column vectors. (The text is a bit sloppy about this in the interest of saving space.) #9.48(b,c) T -
Kent State MATH 41021
MATH 4/51021 Homework #11 Due: Friday, April 24 Reading: For Mon., April 20: 10.4; Problems 10.7, 10.8 For Wed., April 22: 10.5; Problems 10.910.12; Polynomial handout For Mon., April 27: 10.6, 10.7; Problems 10.1310.20 Problems to turn in: 1. Let V -
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Kent State MATH 41021
MATH 4/51021 Homework #12 Due: Friday, May 8* Reading: For Mon., April 27: 10.6, 10.7; Problems 10.1310.20 Problems to turn in: 1. Find all possible Jordan Canonical Forms for a linear operator with the given characteristic polynomial (t) and minimal -
Kent State MATH 41021
MATH 41021 EXAM I Prof. D. L. White February 25, 2009 NAME: Write clearly and SHOW ALL WORK. There are 7 problems, on 5 distinct pages. Put your name on each page. Time allowed is 50 minutes, the exam is worth 100 points. Notation: R denotes the fi -
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Kent State MATH 41021
Math 41021 Exam II Review Exam II will be given in class on Wednesday, April 1, 2009. It will cover Chapters 5 and 6 and 7.17.7, Homework #5#8, and material from class February 18 through March 16 (pages 3466 of the lecture notes). The exam will cons -
Kent State MATH 41021
MATH 4/51021 EXAM II Prof. D. L. White April 1, 2009 NAME: Write clearly and SHOW ALL WORK. There are 7 problems, on 4 distinct pages. Put your name on each page. Time allowed is 50 minutes, the exam is worth 100 points. 1. (20 points) Using comple -
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Kent State MATH 41021
Math 41021 Exam III Review Exam III will be given in class on Wednesday, April 29, 2009. It will cover 9.19.5, 9.79.8, 10.310.4, Homework #9#11, and material from class March 18 through April 20. (pages 67100 of the lecture notes). The exam will cons -
Kent State MATH 41021
THE LLAMA SONG by Burton Earny Heres a llama theres a llama and another little llama fuzzy llama funny llama llama llama duck Llama llama cheesecake llama tablet brick potato llama llama llama mushroom llama llama llama duck I was once a tree house I -
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