A =[6 4] [3 5] 1. Compute the eigenvalues of A. 2. Find the eigenspace Eλ for each eigenvalue λ. Write your answer as the span of a collection of vectors. 3. Verify the set of all eigenvectors of A spans R^2 4. Hence, find an invertable matrix P and a diagonal matrix D such that A = PDP−1 5. Hence, find a formula for efficiently calculating A^n for any integer n ≥ 0. Make your formula as simple as possible.
A =[6 4] [3 5] 1. Compute the eigenvalues of A. 2. Find the eigenspace Eλ for each eigenvalue λ. Write your answer as the span of a collection of vectors. 3. Verify the set of all eigenvectors of A spans R^2 4. Hence, find an invertable matrix P and a diagonal matrix D such that A = PDP−1 5. Hence, find a formula for efficiently calculating A^n for any integer n ≥ 0. Make your formula as simple as possible.
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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Please help me with the below questions and answer in detail with each step:
(Matrix A is of size 2 x 2)
A =[6 4]
[3 5]
1. Compute the eigenvalues of A.
2. Find the eigenspace Eλ for each eigenvalue λ. Write your answer as the span of a collection of
vectors.
3. Verify the set of all eigenvectors of A spans R^2
4. Hence, find an invertable matrix P and a diagonal matrix D such that A = PDP−1
5. Hence, find a formula for efficiently calculating A^n for any integer n ≥ 0. Make your formula
as simple as possible.
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