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-8 2 2 2 -5 4 Problem 1. Let A = 2 4 -5/ (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities. (3) Is A invertible? Why?

-8 2 2 2 -5 4 Problem 1. Let A = 2 4 -5/ (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities. (3) Is A invertible? Why?

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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-8 2 2 Problem 1. Let A = 2 -5 4 2 4 -5/ (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities. (3) Is A invertible? Why? Problem 2. Find a basis for each eigenspace of the matrix A of Problem 1. Problem 3. Find an orthogonal diagonalization of the matrix A of Problem 1. Problem 4. Define a dynamical system with bo = 2 and bn+1 = 3 Abn, for n = 1, 2, 3,..., with A as in Problem 1. Find a formula for b for each n.
Transcribed Image Text:-8 2 2 Problem 1. Let A = 2 -5 4 2 4 -5/ (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities. (3) Is A invertible? Why? Problem 2. Find a basis for each eigenspace of the matrix A of Problem 1. Problem 3. Find an orthogonal diagonalization of the matrix A of Problem 1. Problem 4. Define a dynamical system with bo = 2 and bn+1 = 3 Abn, for n = 1, 2, 3,..., with A as in Problem 1. Find a formula for b for each n.
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