Let A belonging be a non-singular matrix. Let be its characteristic polynomial, = det(tI-A) = . a) Prove that
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Originally Posted by page929 Let A belonging be a non-singular matrix. Let be its characteristic polynomial, = det(tI-A) = . a) Prove that . Now, note that is the result of changing the sign to all columns of A. P.S. The hypothesis non-singular is irrelevant.
By the way, to get all of a subscript or all of a superscript above or below the main level, in LaTeX, put them in { }: e^{ax_{1+1}} gives .
Originally Posted by FernandoRevilla . Now, note that is the result of changing the sign to all columns of A. or, det(-A) = det[(-I)(A)] = det(-I)xdet(A) = ((-1)^n)xdet(A)
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