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November 27th, 2009, 02:39 PM  #1 
Senior Member Joined: Nov 2009 Posts: 169 Thanks: 0  Show that A must be invertible
Let be a polynomial of degree n in x with real coefficients. For any mxm matrix A, we define . Show that, if and , then A must be invertible. [Hint: isolate Im from the equation P(A) = 0m] For A = [2 2 1] [1 1 1] [2 4 1] , compute , if , calculate P(A). ) Can you explan this,>? For p(A), How can I subtract 2 from a mtrix? 
November 28th, 2009, 01:32 AM  #2 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Show that A must be invertible
Subtracting 2 from a matrix is really subtracting 2I... that is P(A) (as a formula on matrices) will be A^2 + A  2I Does that answer your question or is there something I missed? Also, in latex, you can get subscripts as well; just but _ after the letter. E.g. a_0 gives you If you need more than one symbol in the subscript, wrap it in brackets. So A_{0,0} gives you 

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