Suppose we have been given the task of nding the degree 3 polynomial P(:r:) = 013:3 + 113:2 + car: + d which passes through the points (1,1), (0,1), and (1, 3) and satises P'(1) : 3. 1. Show that the coeicients of P, a, b, c, and d satisfy the following system of equations given the four data points above. So 2b + c = 3 a + b c + d : 1 d 1 a+b+c+d : 3 Then use the above information to write the corresponding matrixvector equation As? 2 13'. 1 3 1 2 a '1 z 1 1 I u . I 0 a 1 5 2. Wlthout usmg rowreduction, verify that A1 : 1 5 1 _ _ _ _ 1 _ 2 4 4 0 0 1 0 Please do not show any row reduction steps for this question, otherwise you will not get any credit. 3. Use the previous parts to nd P(:z:)