Could someone please let me know how I would go about accomplishing the following tasks. Thank you.

Let A = [[4,0,0],[0,1,3],[0,3,1]

a) Find the Eigenvalues of A.

(lambda - 4)(lambda - 4)(lambda + 2)

So the eigenvalues are 4, 4, and -2.

b) For each eigenvalue, find a basis for the corresponding eigenspace.

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c) Use these bases vectors to construct an orthogonal matrix P.

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d) Verify that $\displaystyle P^-1AP$ is a diagonal matrix.

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