4) The linear transformation L defined by L(p(x)) = p'(x)+p(0) maps Pinto P. a) Find the...

4) The linear transformation L defined by L(p(x)) = p'(x)+p(0) maps Pinto P. a) Find the matrix representation of L with respect to the ordered bases {1,x,x} and {1, 1-x}. 6 b) For the vector, p(x) = 2x + x - 2 (i) 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 {1,x,x"}. (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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