Consider the following matrices A and B and vector b. D)What is the algebraic and geometric multiplicities of the eigenvalues of A. f) Find A10b by writing b as linear combination of eigenvectors of A. G) Find a formula for Ak for all non-negative integers k. H) Use (g) to find A10b and compare it with what you found in (VI). I) Is A similar to B? If yes, find an invertible matrix such that P−1AP = B.

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