4. Let A = (a) Find all complex eigenvalues of A. (b) s-1AS = B. By what factor does B scale the plane? By what angle does B rotate the plane (counterclockwise about the origin)? Find an invertible matrix S and a rotation-scaling matrix B such that

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 10AEXP
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Question
1
4. Let A =
-1
3
(а)
Find all complex eigenvalues of A.
(b)
s-'AS
Find an invertible matrix S and a rotation-scaling matrix B such that
B. By what factor does B scale the plane? By what angle does B rotate
the plane (counterclockwise about the origin)?
Transcribed Image Text:1 4. Let A = -1 3 (а) Find all complex eigenvalues of A. (b) s-'AS Find an invertible matrix S and a rotation-scaling matrix B such that B. By what factor does B scale the plane? By what angle does B rotate the plane (counterclockwise about the origin)?
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