Let V be the vector space all polynomials of degree 3 with real coefficients in one...

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Let V be the vector space all polynomials of degree 3 with real coefficients in one variable z. (a) Consider the map T: V V defined by T(p(x)) = p(x + a), where a is a fixed real number. Show that T is a linear operator. (b) Let B be the basis {1, t, t/2, /6} for V. Compute MB (T). Let V be the vector space all polynomials of degree 3 with real coefficients in one variable z. (a) Consider the map T: V V defined by T(p(x)) = p(x + a), where a is a fixed real number. Show that T is a linear operator. (b) Let B be the basis {1, t, t/2, /6} for V. Compute MB (T).

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