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B3: Consider the matrix: 3 A =-2 -3 -3 2 -1 -1) a) Find the eigenvalues of A. For each eigenvalue A, find the dimension of the eigenspace ker(A – AI) and give a basis (i.e. find eigenvectors). You are given that (A – 2)(A² + 6A + 8) = A³ + 4x² – 4A – 16. b) Decide if A is diagonalisable. If it is, then write A as: A = PDP-, where D is a diagonal matrix. c) Compute A°. marns)

B3: Consider the matrix: 3 A =-2 -3 -3 2 -1 -1) a) Find the eigenvalues of A. For each eigenvalue A, find the dimension of the eigenspace ker(A – AI) and give a basis (i.e. find eigenvectors). You are given that (A – 2)(A² + 6A + 8) = A³ + 4x² – 4A – 16. b) Decide if A is diagonalisable. If it is, then write A as: A = PDP-, where D is a diagonal matrix. c) Compute A°. marns)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Plz solve c part only in 30 min and take a thumb up plz
B3: Consider the matrix: A = -2 -3 -3 2 -1 -1 a) Find the eigenvalues of A. For each eigenvalue A, find the dimension of the eigenspace ker(A – AI) and give a basis (i.e. find eigenvectors). You are given that (A – 2)(A² +6A + 8) = 13 + 42 – 41 – 16. b) Decide if A is diagonalisable. If it is, then write A as: A = PDP-, where D is a diagonal matrix. c) Compute A". marks)
Transcribed Image Text:B3: Consider the matrix: A = -2 -3 -3 2 -1 -1 a) Find the eigenvalues of A. For each eigenvalue A, find the dimension of the eigenspace ker(A – AI) and give a basis (i.e. find eigenvectors). You are given that (A – 2)(A² +6A + 8) = 13 + 42 – 41 – 16. b) Decide if A is diagonalisable. If it is, then write A as: A = PDP-, where D is a diagonal matrix. c) Compute A". marks)
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