TITLE: Find 2 unknowns in a symmetric matrix given the eigenvector.
QUESTION [1 upvotes]: Find A and B in the symmetric matrix with the given eigenvector below.
New to eigenvector algebra. Read some sections in Schaum Linear Algebra but still cannot figure it out on how to approach this question. Hope some tips on how to get me going. Thanks.

REPLY [0 votes]: If $A$ is the matrix and $b$ the eigenvector then we get
$Ab=(18, A-2,B+8)^T$. Since $Ab=\lambda b$ for some scalar $ \lambda$, we see:
$A-2=0$ , $18= \lambda$ and $B+8=\lambda$. 
Conclusion: $A=2, B=10$ and $ \lambda =18$.
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