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4 -2 2 A = 2 2 -2 4 In this assignment, we will diagonalize A.

4 -2 2 A = 2 2 -2 4 In this assignment, we will diagonalize A.

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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4 -2 2 A = 2 2 2 -2 4 In this assignment, we will diagonalize A. STEP 1: Solve the characteristic equation det(A – AI3) = 0 to find the eigenvalues and their multiplicities. I strongly suggest to use co-factor expansion of the first row! Answer: The smaller one is A1 2 with multiplicity 2 The other (the larger one) is 2 = 4 with multiplicity Reminder: A1 < A2.
Transcribed Image Text:4 -2 2 A = 2 2 2 -2 4 In this assignment, we will diagonalize A. STEP 1: Solve the characteristic equation det(A – AI3) = 0 to find the eigenvalues and their multiplicities. I strongly suggest to use co-factor expansion of the first row! Answer: The smaller one is A1 2 with multiplicity 2 The other (the larger one) is 2 = 4 with multiplicity Reminder: A1 < A2.
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