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Homework Statement
Is the following matrix diagonalizable in R?
[ 2 1 0 ]
[ 1 3 -1 ]
[ -1 2 3 ]
Homework Equations
The Attempt at a Solution
I've checked my work and found one eigenvalue = 2, with the corresponding eigenvector = [1, 0, 1]. My question is -- Because I have one eigenvector, can I conclude that this matrix is diagonalizable in R? If I had two eigenvalues could I say it was diagonalizable in R and R2, or just R2?