(4 1 4 1 4 1 4 4 A 4 -1 1 -1 1 -1 -1 1 (a) Find the characteristic polynomial of A. (b) Find the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A ||

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 9RQ
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(4 1
4 1
4 1
4
4
A =
4
-1 1
-1 1
-1
-1 1
(a) Find the characteristic polynomial of A.
(b) Find the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A.
(c) Find the Ferrer diagram corresponding to each eigenvalue of A.
(d) For each eigenvalue A; of A, find the maximum of nullity((A – A;I)") over all r E N.
Furthermore, determine the smallest r EN to attain the maximum.
Transcribed Image Text:(4 1 4 1 4 1 4 4 A = 4 -1 1 -1 1 -1 -1 1 (a) Find the characteristic polynomial of A. (b) Find the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A. (c) Find the Ferrer diagram corresponding to each eigenvalue of A. (d) For each eigenvalue A; of A, find the maximum of nullity((A – A;I)") over all r E N. Furthermore, determine the smallest r EN to attain the maximum.
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