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tengxiaona
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Homework Statement
Find a 3*3 matrix A which is not diagonalizable and such that 2 is the only eigenvalue of A
Homework Equations
The Attempt at a Solution
since λ=2,and it is a 3*3 matrix
i get the det(λI-A)=(λ-2)^3=0
then λ^3-6λ^2+12λ-8=0
now i use http://image.cramster.com/answer-board/image/cramster-equation-2009452223286337456700835550002161.gifas[/URL] matirx A
and i calculate
det(λI-A)
=λ^3-λ^2(i+e+a)+λ(ai+ae+ie-cg-hf-bd)-(aef+bfg+cdh+cge-ahf-bdi)=0
now we can easy to know that
i+e+a=6
ai+ae+ie-cg-hf-bd=12
aef+bfg+cdh+cge-ahf-bdi=18
now I am stuck here
can anyone help me to slove these equtions.
i don't konw the way i doing this problem is right or wrong.
if u have any others ideas,please help me
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