My Math Forum AE=ED (Invertible and Diagonal Matrix)

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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 non-zero 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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