2. Given the following matrix A, 9 -6 3 -7 14 -10 6 -14 24 -18 11-24 8 -6 3 -6 Find matrices D and P such that A = D= P= PDKP-1 1 2 31 1 2 2 1 3226 2 32 P"= 2 2 -7 4 14 -8 -1 5 -3 2 -15
Although the answers are provided, I'm still confused about how to solve for D and P. Any help would be greatly appreciated, and thanks in advance.
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In Step 2 (Description of the steps), I see that you're finding the eigen values of matrix A. I see that you set A - (lambda)i = 0. Next you say "Solving this, we get
(lambda2-1) (lambda-2)2 = 0 ---> lambda = 1, -1, 2, 2". Can you please explain how solved to get the "(lambda2-1) (lambda-2)2 = 0 ---> lambda = 1, -1, 2, 2" ?
I thought that I was supposed to find the characteristic polynomials (the values from the diagonals - in this case, 9-lambda, -10-lambda, etc.), set them equal to zero (9-lambda=0, -10-lambda=0, etc.) solve for the lambda values (lambda=9, lambda=-10, etc.), and use those lambda values in the D matrix.
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