1. Consider the polynomials ta ask P11. Use Mathematica to: ona e has able t ssal e tas (a) Compute the change of basis matrix PB-S. sessab ask ssessable (b) Compute the change of basis matrix PS- B. Assess op as bk (2) := (1 - x ) kyll-k tas (c) Find the coordinate vector of the polynomial Mo's e sa for k = 0, 1, . .. , 11, and let B = {bo, b1,. . ., bil}. It can be shown that B is a basis for P11, the vector space of polynomials of degree with respect to the basis B. Monash U sa b at most 11. (You do not need to prove this.) Let PK (x) = ack for k = 0, 1, . . ., 11, so that S = {Po, P1, .. ., pil} is the standard basis for Mo n ash Uni ble tas Cop t Mon ash Univ vers task, Cop Ionash Ur sk. Copy Ionash ht Mor U niversity Ionash University Ass Copyri Ionash Uni sity 20 S 1( 2 ) = 2 + 223 -224 +27 Copyright pyright onash U Unive 2 2 es sab right Mozz vers 2021 Hint: You may find the Mathematica command CoefficientList [p (x) , x] useful. For a given polynomial Mon ers 21, As [(2 marks, MTH2021) , (2 marks, MTH2025)] Monas *2 Asses p(x) = Co + cix + c2x2 + ...+ Cnx in x, CoefficientList [p (x) , x] returns the list of coefficients { co, c1, . . ., Cn}. Ionash U ive 20 Assess 202 [(2 marks, MTH2021) , (1 mark, MTH2025)] ash Universi ssessab University University AS niversity [(2 marks, MTH2021) , (1 mark, MTH2025)] ersity 2021 sity 2021 202