Let A = egin{bmatrix} 1 & -4 & 6 \ 0 & -1 & 0 \ 0 & 0 & -1 end{bmatrix} and P = egin{bmatrix} 1 & 2 & -3 \ 0 & 1 & 0 \ 0 & 0 & 1 end{bmatrix}. Given that P diagonalizes A, then compute each of the following powers of A. (a) A^{380} = egin{pmatrix} ? & ? & ? \ ? & ? & ? \ ? & ? & ? end{pmatrix} (b) A^{-380} = egin{pmatrix} ? & ? & ? \ ? & ? & ? \ ? & ? & ? end{pmatrix}
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Now, we need to compute A^380 and A^38. Since D = A, we can compute these powers directly: Show more…
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