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4. Given the eigenvalues of a matrix:

a) Determine the characteristic polynomial.

b) Find vectors than can act as bases for the associated eigenspaces.

Part a seems relatively straight forward but for part b I wondering if you need to be given a matrix along with the eigenvalue. Or is there a way where if you are just given eigenvalues that you can find bases for eigenspaces without the matrix. Almost seems impossible but i just figured I would ask.

Thanks!