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4) The linear transformation L defined by L(p(x)) = p'(x)+ p(0) maps P, into P. a)...


4) The linear transformation L defined by L(p(x)) = p(x)+ p(0) maps P, into P. a) Find the matrix representation of L with r
b) For the vector, p(x) = 2x2 + x-2 () find the coordinates of L(p(x)) with respect to the ordered basis {1, 1-x}., using the
4) The linear transformation L defined by L(p(x)) = p'(x)+ p(0) maps P, into P. a) Find the matrix representation of L with respect to the ordered bases {1xx.x"} and {1, 1-x}
b) For the vector, p(x) = 2x2 + x-2 () find the coordinates of L(p(x)) with respect to the ordered basis {1, 1-x}., using the matrix you found in a). Remember to use the coordinate vector of p(x) with respect to the basis {1xx"}. (ii) Show that they are the weights that work by writing the linear combination with the basis elements and comparing the resulting polynomial to L(p(x))
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Given: The linear transformation is, L(P(x))= p(x)+ p(0) maps pz to P2. a) The matrix representation of the above linear trab) The coordinates of L(P(x)), where p(x)=2x²+x-2. The polynomial p(x) can be written as, P(x)=-2(1)+1(x)+2(x²) Now, computec) Consider the second-degree polynomial p(x) = ax +bx+c. L(P(x)) = 2 ax +b+c Represent the above polynomial into basis eleme

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