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.
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
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 29EQ
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff608864a-3637-4689-8f45-1452309743a1%2F310ab981-0e6a-49e3-ab90-fa11dd566f14%2Fjxykdw_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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