2. x(t)=a+bt+Ct2 € P2 LO L(x(t))=a+(a+2b)t+(a+2c)t2 € P2 input Abstract mathematics A(matrix) output S = {1+t, 1- t t?}

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2 X T A Bt Ct2 P2 Lo L X T A A 2b T A 2c T2 P2 Input Abstract Mathematics A Matrix Output S 1 T 1 T T 1 (68.77 KiB) Viewed 36 times

2. x(t)=a+bt+Ct2 € P2 LO L(x(t))=a+(a+2b)t+(a+2c)t2 € P2 input Abstract mathematics A(matrix) output S = {1+t, 1- t t?} is a basis for P2. Y = A1. Y = [L(x(t))]s 3 x 1 vector X = ( xls 3x1 vector The above figure shows a system L with inputs and outputs belonging to the P_2 function space as a matrix with respect to the basis S of P_2. (a) Describe the process for finding X and indicate its value. (b) Describe the process for finding A1 and indicate its value. (c) Describe the process for finding Y and indicate its value. (d) Is the above system L one-to-one? Briefly explain. (e) is the above system L onto? Briefly explain.