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3 1. Let A = 9 -2 -6

3 1. Let A = 9 -2 -6

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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5.1: Eigenvectors and Eigenvalues

 

a) The eigenvalues are 0 and -3. Compute and sketch the two eigenspaces.

b) On the same plot, sketch the vector x = [−6   2]T and the vector Ax. What is the action of A on a vector x in the eigenspace for λ = 0?

c) On the same plot, sketch the vector y = [3   −2]T and the vector Ay. What is the action of A on a vector y in the eigenspace for λ = −3?

d) Write one vector z in R2 such that the product Az both scales and rotates the vector z.

- [3 의 9 1. Let A -2 -6
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