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Let A be a diagonalizable n x n matrix and let P be an invertible n...

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = p-1AP is the diagonal form of A.

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = p-1AP is the diagonal form of A. Prove that A* = Pokp-1, where k is a positive integer. Use the result above to find the indicated power of A. 10 18 A = -6 -11 18].46 A = 11
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Let A be a diagonalize nan matsia and let p be an investible nan mation such that B = PAP B is the diagonal forms of A. mult10 16 for eigen values (d), det (A-d I) TO 10-1 1 A-dl= -6 11-d (10-1) (-11-d) + 10b=0 d+d-110 + 108=0 +1800 dtd-250 i de-a dlet t=3 and t=1 we get 5 3 P th & IP= -3+4=1 e pt = I adj p = adj p = & BE PI 3 A = PB pt - AO = PBR (26 o 3 3 192 lo -18 -19

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