5 4 23. Consider the matrix A =4 5 2[2 2 2](a) Find the characteristic polynomial det(A– AI) = 0, and show that it has one distinctreal root = 10, and a double root = 1.(b) Find a line such that any point x on the line would be mapped back onto the sameline by the linear mapping Ax, where k is a positive integer.(c) Find a plane such that any point x on the plane would be mapped back onto thesame plane by the linear mapping A^x, where k is a positive integer.

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Answered: 5 4 2 3. Consider the matrix A = 4 5 2.…

5 4 2 3. Consider the matrix A = 4 5 2. 2 2 2 (a) Find the characteristic polynomial det(A– AI) = 0, and show that it has one distinct %3D real root A = 10, and a double root A = 1.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 16EQ

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Question

5 4 2
3. Consider the matrix A =
4 5 2
[2 2 2]
(a) Find the characteristic polynomial det(A– AI) = 0, and show that it has one distinct
real root = 10, and a double root = 1.
(b) Find a line such that any point x on the line would be mapped back onto the same
line by the linear mapping Ax, where k is a positive integer.
(c) Find a plane such that any point x on the plane would be mapped back onto the
same plane by the linear mapping A^x, where k is a positive integer.

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