Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Chapter 4.1, Problem 5EQ

In Exercises 1-6, show that v is an eigenvector of A and find the corresponding eigenvalue.

A = [ 3 0 0 0 1 − 2 1 0 1 ] , v = [ 2 − 1 1 ]

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Chapter 4 Solutions

Linear Algebra: A Modern Introduction

Ch. 4.1 - In Exercises 1-6, show that is an eigenvector of A...Ch. 4.1 - In Exercises 1-6, show that vis an eigenvector of...Ch. 4.1 - Prob. 3EQCh. 4.1 - In Exercises 1-6, show that vis an eigenvector of...Ch. 4.1 - In Exercises 1-6, show that vis an eigenvector of...Ch. 4.1 - In Exercises 1-6, show that is an eigenvector of A...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...
Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 23-26, use the method of Example 4.5...Ch. 4.1 - In Exercises 23-26, use the method of Example 4.5...Ch. 4.1 - In Exercises 23-26, use the method of Example 4.5...Ch. 4.1 - In Exercises 31-34, find all of the eigenvalues of...Ch. 4.1 - Prob. 32EQCh. 4.1 - In Exercises 31-34, find all of the eigenvalues of...Ch. 4.1 - Consider again the matrix A in Exercise 35. Give...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Prob. 24EQCh. 4.2 - Prob. 26EQCh. 4.2 - Prob. 27EQCh. 4.2 - In Exercises 26-34, use properties of determinants...Ch. 4.2 - Prob. 29EQCh. 4.2 - Prob. 30EQCh. 4.2 - Prob. 31EQCh. 4.2 - In Exercises 26-34, use properties of determinants...Ch. 4.2 - Prob. 33EQCh. 4.2 - In Exercises 26-34, use properties of determinants...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 - Find the determinants in Exercises 35-40,...Ch. 4.2 - Prob. 45EQCh. 4.2 - In Exercises 45 and 46, use Theorem 4.6 to find...Ch. 4.2 - In Exercises 47-52, assume that A and B are nn...Ch. 4.2 - In Exercises 47-52, assume that A and B are n n...Ch. 4.2 - In Exercises 47-52, assume that A and B are n ×...Ch. 4.2 - In Exercises 47-52, assume that A and B are n × n...Ch. 4.2 - In Exercises 47-52, assume that A and B are nn...Ch. 4.2 - In Exercises 47-52, assume that A and B are nn...Ch. 4.2 - Prob. 53EQCh. 4.2 - Prob. 57EQCh. 4.2 - Prob. 58EQCh. 4.2 - Prob. 59EQCh. 4.2 - In Exercises 57-60, use Cramer's Rule to solve the...Ch. 4.2 - Prob. 61EQCh. 4.2 - Prob. 62EQCh. 4.2 - Prob. 63EQCh. 4.2 - Prob. 64EQCh. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - Prob. 2EQCh. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - Prob. 7EQCh. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.4 - Prob. 5EQCh. 4.4 - Prob. 6EQCh. 4.4 - Prob. 7EQCh. 4.4 - In general, it is difficult to show that two...Ch. 4.6 - Let x=x(t) be a twice-differentiable function and...
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