1). suppose that y1, y2, y3 are the eigenvalues of a 3 by 3 matrix A, and suppose that u1, u2,u3 are corresponding eigenvectors. Prove that if { u1, u2, u3 } is a linearly independent set and if p(t) is the characteristic polynomial for A, then p(A) is the zero matrix.(adsbygoogle = window.adsbygoogle || []).push({});

I thought cayley-hamilton theorem simply states that if p(t) is the characteristic polynomial for A, then p(A) is the zero matrix. do the eigenvectors have to be learly independent for this to be true? i thought it was true in all cases.

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# Eigenvalues, eigenvectors question

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