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April 14th, 2010, 02:13 PM   #1
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AE=ED (Invertible and Diagonal Matrix)

I am having trouble with the following question. I am able to do parts (a) and (c) but am unable to figure out parts (b) and (d).

A=[ 6 5] (2x2 Matrix)
__[-3 -2]

(a) Find the eigenvalues and eigenvectors of A.
(b) Find a diagonal matrix D and an invertible matrix E such that AE=ED.
(c) Calculate A^100 .
(d) Express the determinant of A in terms of the eigenvalues of A.

Please can somebody help me.
Thanks,
paulyc2010 is offline  
 
April 14th, 2010, 03:18 PM   #2
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Re: AE=ED (Invertible and Diagonal Matrix)

E, it turns out, is nothing more than the eigen vectors written as columns, and E inverse is the inverse of E.
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April 14th, 2010, 03:19 PM   #3
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Re: AE=ED (Invertible and Diagonal Matrix)

Although, while we're on it - how did you do c without b?
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April 15th, 2010, 07:18 AM   #4
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The non-zero elements of D are the eigenvalues of A.
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April 18th, 2010, 02:50 PM   #5
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Re: AE=ED (Invertible and Diagonal Matrix)

Thanks guys for that, was a great help.
paulyc
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