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Let T be a linear operator on a finite-dimensional vector space, and let p(t) be the

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

Solution for problem 8 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 8

Let T be a linear operator on a finite-dimensional vector space, and let p(t) be the minimal polynomial of T. Prove the following results. (a) T is invertible if and only if p(0) - 0. (b) If T is invertible and p(t) = tn + a n _in _ 1 + + ait + a 0 , then T - 1 = - (T"- 1 + a n _,Tn - 2 + + a 2T + a,I)

Step-by-Step Solution:
Step 1 of 3

MATH121 Chapter 2 Notes LESSON 2.1 – Linear Equations in One Variable Example 1. 6(5x - 5) = -31(3 - x) (Multiply 6 and 5x, and 6 and -5) (Multiply -31 and 3, and -31 and –x) 30x - 30 = -93 + 31x (Get similar values on same sides) -x = -63 (Divide by -1 to get x by itself) x = 63 (One Solution!) Example 2. 3.4x + 5 = 4.4x (Subtract 3.4x from 4.4x to get the similar values on the same side) 5 = x (One solution!) Example 3. (2z - 9)/5 – (1/10) = (-13z + 12)/10 (Since each is a fraction, you can easily see the similar denomina

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Chapter 7.3, Problem 8 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, and let p(t) be the