Let T element of L(R3 ) such that -4, 5 and square root 7 are its eigenvalues.
Show that T(x) - 9x = (-4, 5, square root 7).
Since T has at most 3 distinct eigenvalues , the hypothesis imply that 9 is not an eigenvalue of T.
Thus T − 9I is surjective. In particular, there exists such that
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