標題:
Matrix problem
A= -2 2 3 -2 3 2 -4 2 5 (a) Find an invertible matrix P and a diagonal matrix D such that D = (P^?1)AP. (b) Compute A^5. 更新: A should be 3 -1 0 -1 2 -1 0 -1 3
最佳解答:
Using |A-λI|=0 and we find that λ=1,3,4 when λ=1, the eigenvector is (1,2,1) when λ=3, the eigenvector is (1,0,-1) when λ=4, the eigenvector is (1,-1,1) So D is 1 0 0 0 3 0 0 0 4 P is 1 1 1 2 0 -1 1 -1 1 (b) A^5=[PDP^(-1)]^5=PD^5P^(-1) the result is 463.000 -341.000 220.000 -341.000 342.000 -341.000 220.000 -341.000 463.000
其他解答:7638E748CCC65837
Matrix problem
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發問:A= -2 2 3 -2 3 2 -4 2 5 (a) Find an invertible matrix P and a diagonal matrix D such that D = (P^?1)AP. (b) Compute A^5. 更新: A should be 3 -1 0 -1 2 -1 0 -1 3
最佳解答:
Using |A-λI|=0 and we find that λ=1,3,4 when λ=1, the eigenvector is (1,2,1) when λ=3, the eigenvector is (1,0,-1) when λ=4, the eigenvector is (1,-1,1) So D is 1 0 0 0 3 0 0 0 4 P is 1 1 1 2 0 -1 1 -1 1 (b) A^5=[PDP^(-1)]^5=PD^5P^(-1) the result is 463.000 -341.000 220.000 -341.000 342.000 -341.000 220.000 -341.000 463.000
其他解答:7638E748CCC65837
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