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Dissonance in E
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Homework Statement
I have matrix
A = 4 2
0 1
Whose eigenvalues I found to be 4 & 1
I need to find the eigenvectors for the same matrix
Homework Equations
(A-lambdaI)V=0
The Attempt at a Solution
Lambda = 4 gives
0 2 x V1 = 0
0 -3 V2
0v1 + 2v2 = 0
0v1 - 3v2 = 0
Eigenvector = 0 , 0
How does that give me any choice? Either there's some fundamental rule I am missing or my maple skills need a workout as according to maple the vector is 1, 0
which would give 1+0 = 0 ? No?
Lambda = 1 gives
3 2 x V1 = 0
0 0 V2
3v1 + 2v2 = 0
0v1 + 0 v2 = 0
eigenvector = -2, 3
Ok I get that this works, why couldn't I say that the eigenvector is 2, -3?
wouldnt this give 3(2) + 2(-3) = 0
Whats the difference?
Clarifications greatly appreciated.
P.s: Sorry for the painful format, couldn't figure out how to draw matrices with latex.
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