1 has eigenvalues A₁ = -1 and A₂ = 3. The bases of the eigenspaces are v₁ = [¹] 7 the matrix A = -32 Find an invertible matrix S and a diagonal matrix D such that S¹AS = D. and v₂ = , respectively. S= D

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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7
13
the matrix A=
1
-32 -5
Find an invertible matrix S and a diagonal matrix D such that S-¹AS = D.
has eigenvalues A₁ = -1 and A₂ = 3. The bases of the eigenspaces are v₁ =
[]
www
and v₂ -
1
, respectively.
5 =
D=
6
Transcribed Image Text:7 13 the matrix A= 1 -32 -5 Find an invertible matrix S and a diagonal matrix D such that S-¹AS = D. has eigenvalues A₁ = -1 and A₂ = 3. The bases of the eigenspaces are v₁ = [] www and v₂ - 1 , respectively. 5 = D= 6
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