1. Consider the polynomials for k = 0,1, ..,11, and let B = {bo,b1,., bị1}. It can be shown that B is a basis for P11, the vector space of polynomials of degree at most 11. (You do not need to prove this.) Let pr (x) = x* for k = 0, 1,., 11, so that S = {po,P1,...,P11} is the standard basis for P11. Use Mathematica to: Monas onash ash ask (a) Compute the change of basis matrix PB→s. task (b) Uni sable ta essae task (c) Find task Copyn pyr Compute the change of basis matrix PsR. Gers br (x) := (1 – x)*g11-k the coordinate vector of the polynomial Assessable Ass Monash Monash Univ with a respect to the basis B. cht Monash Univer Hint: You may find the Mathematica command CoefficientList [p(x),x] useful. For a given polynomial p(x) = co +c1x + c2x² + · .+ Cnx" in x, CoefficientList [p(x),x] returns the list of coefficients {co,c1, ..,Cn}. task op sessa Ssessa Gessab sable able University able t le tash Copy ht Monash Universi Copye Copyrige Monash U 2021 nash niv ight Moneh U Monas iv 2710 2021 sh Universi University ersity ple t Ssessabl sable Asse pyright yright Monash onash Univer versity 202 ersity 2021.

Which is the definition of a reflexive relation? x ~ Y ⇒ y ~ x for all x, y = X. x~ x for some x E X. x~ x for all x € X. x~y and y~z⇒ x~z for all x, y, z € X. None of the above

Pls help ASAP in whole question and pls make sure to show all steps and details and work.

Is the upside T supposed to be a 1? Kind of confusing

this is very hard to read can someone please rewrite this but type instead of using a pen