- #1

Bkkkk

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## Homework Statement

Given Matrix B:

[ 1 2 1]

[-1 2 -1]

[ 2 -2 3]

and knowing that one of the Eigenvalues is 4, find one other value and its corresponding eigenvector

## Homework Equations

Bx=Lx (The basic idea behind eigenvectors)

det(B-LI)=0

## The Attempt at a Solution

Ive set up the above determinant

[ 1-L 2 1]

[-1 2-L -1]

[ 2 -2 3-L]

Equal to zero, the only way I could figure how to do this question was using long division after getting the characteristic equation, but I keep getting a remainder which I shouldn't get If I am not making a huge mistake.

For the determinant I get either -L^3 + L^2 -9L +3 or -L^3 + 6L^2 -11L + 6

but I checked both using a calculator and long division and both of them give me a remainder.

I don't want the answer flat out maybe point out where I am going wrong, this problem has been bugging me for ages and I really want to know what the hell is wrong.

Thanks