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I'm tasked with finding the characteristic equation, eigenvalues, and bases for the eigenspaces of this matrix [1,...

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Advance Math

I'm tasked with finding the characteristic equation,eigenvalues, and bases for the eigenspaces of this matrix

[1, -3, 3]

[3,-5,3]

[6,-6,4]

After working on the problem, I believe the characteristicequation is (? + 2)^2(?-4), giving eigenvalues of -2 and 4 (pleasecorrect me if I'm wrong). However, I'm lost when finding the basesfor the eigenspace because I'm not sure the eigenvectors I get arelinearly independent.

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