25 Suppose that A = (²5) 05 Find the eigenvector v₁ with respect to the smallest eigenvalue and the eigenvector v2 with respect to the biggest eigenvalue. Make sure all vector entries are integers with no common factor and the first component of each eigenvector is positive. Let S = [1, 2]. Enter all cells for S.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 77E
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Refer to image below along with questions listed here 

a. Whats S =

b. S^−1=

c. Using part a and b, find the diagonal matrix D for which A= SDS^ -1 find what D =

25
(²5).
05
Suppose that A =
Find the eigenvector
with respect to the smallest eigenvalue
and the eigenvector v₂ with respect to the biggest eigenvalue.
Make sure all vector entries are integers with no common factor and the first component of each
eigenvector is positive.
Let S = [v1, v2]. Enter all cells for S.
Transcribed Image Text:25 (²5). 05 Suppose that A = Find the eigenvector with respect to the smallest eigenvalue and the eigenvector v₂ with respect to the biggest eigenvalue. Make sure all vector entries are integers with no common factor and the first component of each eigenvector is positive. Let S = [v1, v2]. Enter all cells for S.
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