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Avinash
Lv 7
Find eigenvalue of A^3 - 2A + 4I given eigenvalue of A?
Update:
A is a 2X2 matrix. It has an eigenvalue = 2 with associated eigenvector
1
-1
Find an eigenvalue and the associated eigenvector of B = A^3 - 2A + 4I
1 Answer
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- ?Lv 74 years ago
If λ,x are an eigenpair of A then Ax=λx
Multiply by A repeatedly and use Ax=λx to get Aⁿx=λⁿx
∴ (A³−2A+4)x = A³x−2Ax+4x = (λ³−2λ+4)x
This means λ³−2λ+4,x are an eigenpair for B
For x=<1,-1>, λ=2 you get for B <1,-1> and 8-4+4=8
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