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19 Nov 2019
Let V = P lessthanorequalto 3 be the set of all polynomials in indeterminate x of degree lessthanorequalto 3, and a zero polynomial. Let D: V rightarrow V be a map defined by D (p (x)) = -p(x) + x middot d/dx p(x). a. Prove that D is a linear transformation of V. b. Let B = {1, x, x^2, x^3} be a basis of V. Write down the matrix of D in this basis. c. Find ker D and im D. Write down their bases in terms of polynomials from V.
Let V = P lessthanorequalto 3 be the set of all polynomials in indeterminate x of degree lessthanorequalto 3, and a zero polynomial. Let D: V rightarrow V be a map defined by D (p (x)) = -p(x) + x middot d/dx p(x). a. Prove that D is a linear transformation of V. b. Let B = {1, x, x^2, x^3} be a basis of V. Write down the matrix of D in this basis. c. Find ker D and im D. Write down their bases in terms of polynomials from V.
hamza2005400Lv2
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Irving HeathcoteLv2
29 Jul 2019
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