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November 27th, 2009, 02:39 PM   #1
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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?
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November 28th, 2009, 01:32 AM   #2
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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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