(a) Assume T: R² → R is a linear transformation with T(1,0) = 3 and T(0, 1) = -1. Calculate T(2,5). (b) Given that the linear transformation T : R³ → R² is defined by T(x, y, z) = (x, z), find ker T. (c) Let C be the vector space of continuous real-valued functions on R. If T: C → C is defined so T(f(x)) = [ƒ (x)], is T a linear transformation? Explain why or why not.

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