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1 -B 1 Are u = and v= 10 0 eigenvectors of 1 02 ? If so, find the eigenvalue

1 -B 1 Are u = and v= 10 0 eigenvectors of 1 02 ? If so, find the eigenvalue

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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Are u = 1 H and v= H eigenvectors of 1 1 02 ? If so, find the eigenvalue.
Transcribed Image Text:Are u = 1 H and v= H eigenvectors of 1 1 02 ? If so, find the eigenvalue.
Example 1: Is it an Eigenvector of A? 6 N Are u = and v= 3 Q -2 eigenvectors of A = A vector x is an eignevector of A if and only if the system Ax =λx is consistent (A is the unknown) Au= [ $ $ ] [ ³5 ] = [ 26 ] 20 1 6 [1 5 2 So u is an eigenvector of A with eigenvalue -4. du 24 REF 6 ~ = [₁8+] => [ ²5 | 26 ] ~ [ 1² ] - ·24 20 -5 20 => 1=-4 consistent 16 3 52 Av = [1 ²][²³] = [1] --[H]=>]-[³] 11 tv=l ∙31 So v is not an eigenvector of A 05 0=5 system is inconsistent
Transcribed Image Text:Example 1: Is it an Eigenvector of A? 6 N Are u = and v= 3 Q -2 eigenvectors of A = A vector x is an eignevector of A if and only if the system Ax =λx is consistent (A is the unknown) Au= [ $ $ ] [ ³5 ] = [ 26 ] 20 1 6 [1 5 2 So u is an eigenvector of A with eigenvalue -4. du 24 REF 6 ~ = [₁8+] => [ ²5 | 26 ] ~ [ 1² ] - ·24 20 -5 20 => 1=-4 consistent 16 3 52 Av = [1 ²][²³] = [1] --[H]=>]-[³] 11 tv=l ∙31 So v is not an eigenvector of A 05 0=5 system is inconsistent
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