Find the eigenvalues and eigenvectors of A geometrically over the real numbers R. (If an eigenvalue does not exist, enter DNE. If an eigenvector does not exist, enter DNE in any single blank.) (reflection in the line y = x) 0 1 A = 1 0 11 1 = 1 x has eigenspace span (smaller A-value) 1 1 12 = -1 × has eigenspace span (larger A-value) -1

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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Find the eigenvalues and eigenvectors of A geometrically over the real numbers R. (If an eigenvalue does not exist, enter DNE. If an eigenvector does not exist, enter DNE in any single blank.)
(reflection in the line y = x)
0 1
A =
1 0
11
1
= 1
x
has eigenspace span
(smaller A-value)
1
1
12
= -1
×
has eigenspace span
(larger A-value)
-1
Transcribed Image Text:Find the eigenvalues and eigenvectors of A geometrically over the real numbers R. (If an eigenvalue does not exist, enter DNE. If an eigenvector does not exist, enter DNE in any single blank.) (reflection in the line y = x) 0 1 A = 1 0 11 1 = 1 x has eigenspace span (smaller A-value) 1 1 12 = -1 × has eigenspace span (larger A-value) -1
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