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Let T be a linear operator on a finite-dimensional vector space V, and let x be a

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence ISBN: 9780130084514 53

Solution for problem 15 Chapter 7.3

Linear Algebra | 4th Edition

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Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

Linear Algebra | 4th Edition

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Problem 15

Let T be a linear operator on a finite-dimensional vector space V, and let x be a nonzero vector in V. Prove the following results. (a) The vector x has a unique T-annihilator. (b) The T-annihilator of X divides any polynomial git) for which 9(T) = T(). (c) If p(t) is the T-annihilator of x and W is the T-cyclic subspace generated by x, then />(

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Step 1 of 3

Math 340 Lecture – Introduction to Ordinary Differential Equations – March 28 , 2016 th What We Covered: 1. Worksheet 9 a. Highlights i. We went over a lot of the problems in class but the rest of the work sheet was homework so I won’t be giving the answers on here 2. However, the general way to solve the problems on the work sheet and for the upcoming quiz is: a. Assuming you have the equation = where A is a square matrix i. First, find the eigenvalue = (−1) det − = 0 ii. From there we can find the eigenvector by ( − ) b. We can then format the final solution exponentially:

Step 2 of 3

Chapter 7.3, Problem 15 is Solved
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Textbook: Linear Algebra
Edition: 4
Author: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence
ISBN: 9780130084514

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Let T be a linear operator on a finite-dimensional vector space V, and let x be a