SOLUTION: Let A= [-8 6 0; -9 7 0; 27 -18 1]. Find an invertible matrix X and a diagonal matrix D such that D=X^−1AX.

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Question 1161348: Let A= [-8 6 0; -9 7 0; 27 -18 1]. Find an invertible matrix X and a diagonal matrix D such that D=X^−1AX.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
First diagonalize matrix A, that is find

D and X such that 

A=X%2AD%2AX%5E%28-1%29

Left-multiply both sides by X-1

X%5E%28-1%29%2AA=X%5E%28-1%29%2AX%2AD%2AX%5E%28-1%29

Right multiply both sides by X

X%5E%28-1%29%2AA%2AX=X%5E%28-1%29%2AX%2AD%2AX%5E%28-1%29%2AX

Re=group which we can do because matrix multiplication is associative.

X%5E%28-1%29%2AA%2AX=%28X%5E%28-1%29%2AX%29%2AD%2A%28X%5E%28-1%29%2AX%29

X%5E%28-1%29%2AA%2AX=I%2AD%2AI%29

X%5E%28-1%29AX=D

D=X%5E%28-1%29%2AA%2AX

Now you diagonalize A.  If you need help let me know below
and I'll get back to you by email.

Edwin