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12 Nov 2019
Let P_n denote the vector space of all polynomials with real coefficients and of degree at most n for n belongsto N. Define a function T: P_2 rightarrow P_3 by T(p)(x) = x^2 d/dx p(x), for all p(x) belongsto P_2. In addition, let B = {l, x, x^2} be the standard basis of P_2 and let C = {1, x, x^2, x^3} be the standard basis of P_3. (a) Find T(p) with p(x) = 2x^2 + x - 1. (b) Show that T: P_2 rightarrow P_3 is a linear transformation. (c) Find the matrix A for which [T(p(x))]_C = A [p(x)]_B for all p(x) belongsto P_2.
Let P_n denote the vector space of all polynomials with real coefficients and of degree at most n for n belongsto N. Define a function T: P_2 rightarrow P_3 by T(p)(x) = x^2 d/dx p(x), for all p(x) belongsto P_2. In addition, let B = {l, x, x^2} be the standard basis of P_2 and let C = {1, x, x^2, x^3} be the standard basis of P_3. (a) Find T(p) with p(x) = 2x^2 + x - 1. (b) Show that T: P_2 rightarrow P_3 is a linear transformation. (c) Find the matrix A for which [T(p(x))]_C = A [p(x)]_B for all p(x) belongsto P_2.
Nestor RutherfordLv2
11 Apr 2019