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Let f : R* -> R be a linear transformation. (a) If f is invertible and S is a smooth surface, prove that f( S)

Let f : R* -> R be a linear transformation. (a) If f is invertible and S is a smooth surface, prove that f( S) is a smooth surface. (b) If f fails to be invertible, must f(S ) be a smooth surface? Justify your answer with a proof or counterexample

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