Let A be a 3x3 matrix with real entries such that A^2 - 5A + 6I = 0, where I is the 3x3 identity matrix. Let f(x) = det(xI -

A) be the characteristic polynomial of A. a) Find the eigenvalues of A.

b) Find a basis for each eigenspace of A.

c) Use the eigenvalues and eigenvectors to diagonalize A.

d) Use the diagonalization of A to compute the integral of e^(2t)A^t dt from 0 to infinity.

need answer rn.
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