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a) Show that V₁ - A = 0 0 -2 01 3 is an eigenvector of A and find the corresponding eigenvalue. (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.

a) Show that V₁ - A = 0 0 -2 01 3 is an eigenvector of A and find the corresponding eigenvalue. (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.

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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a) Show that V₁ - A = 0 0 -2 01 3 is an eigenvector of A and find the corresponding eigenvalue. (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
Transcribed Image Text:a) Show that V₁ - A = 0 0 -2 01 3 is an eigenvector of A and find the corresponding eigenvalue. (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
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