Question: Let A be a 3 3 matrix with the property that det(A xI3) = (x a)(x b)(x c) where a, b, c R are constants

Let A be a 3 3 matrix with the property that det(A xI3) = (x a)(x b)(x c) where a, b, c R are constants and x is a variable. Show that the transformation T given by x 7 Ax is one-to-one if and only if all of a, b, c are non-zero.

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