"Let T be a the transformation on V = C^3 given by the equation(adsbygoogle = window.adsbygoogle || []).push({});

T(x)=-y-2z

T(y)=3x+5y+7z

T(z)=-2x-3y-4z

where (x,y,z) denotes the standard basis. Find the eigenvalues of T and the corresponding eigenspaces."

Is there a way to find the eigenvalues without solving the 3 equations? How do I find the characteristic polynomial of T without resorting to anything related to determinants?

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# Homework Help: How do I find the characteristic polynomial

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