Question 4 (Unit 5) 21 marks (a) Find the eigenvalues and eigenvectors of the matrix A = H - (b) Express the vector v = [4 4]T in the form av₁ + Bv2, where v₁ are the eigenvectors that you found in part (a). (c) Hence, or otherwise, calculate the product A ¹0 v. and v2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.5: Iterative Methods For Computing Eigenvalues
Problem 16EQ
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Question 4 (Unit 5)
21 marks
(a) Find the eigenvalues and eigenvectors of the matrix
A =
H
4
-
v2
(b) Express the vector v = [4 4] in the form av₁ + Bv2, where v₁ and v₂
are the eigenvectors that you found in part (a).
(c) Hence, or otherwise, calculate the product A 10 v.
Transcribed Image Text:Question 4 (Unit 5) 21 marks (a) Find the eigenvalues and eigenvectors of the matrix A = H 4 - v2 (b) Express the vector v = [4 4] in the form av₁ + Bv2, where v₁ and v₂ are the eigenvectors that you found in part (a). (c) Hence, or otherwise, calculate the product A 10 v.
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