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April 14th, 2010, 02:13 PM  #1 
Newbie Joined: Apr 2010 Posts: 2 Thanks: 0  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, 
April 14th, 2010, 03:18 PM  #2 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  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.

April 14th, 2010, 03:19 PM  #3 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: AE=ED (Invertible and Diagonal Matrix)
Although, while we're on it  how did you do c without b?

April 15th, 2010, 07:18 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,037 Thanks: 2274 
The nonzero elements of D are the eigenvalues of A.

April 18th, 2010, 02:50 PM  #5 
Newbie Joined: Apr 2010 Posts: 2 Thanks: 0  Re: AE=ED (Invertible and Diagonal Matrix)
Thanks guys for that, was a great help. paulyc 

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