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Vectors & Spaceshard
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Let VVV be the vector space of all polynomials of degree at most 333. Consider the linear transformation D:V→VD: V \to VD:V→V defined by D(p(x))=p′(x)−2p(x)D(p(x)) = p'(x) - 2p(x)D(p(x))=p′(x)−2p(x). What is the matrix representation of DDD relative to the standard basis B={1,x,x2,x3}B = \{1, x, x^2, x^3\}B={1,x,x2,x3}?