Then look up thedefinitionsfor yourself! What vector would you get if you take a= 1, b= c= d= 0? What about b= 1, a= c= d= 0? Also try c= 1, a= b= d= 0 and d= 1, a= b= c= 0. Are those vectors linearly independent? If not, can you find a linearly independent subspace?

Any "polynomial of degree at most 5" can be written as . f(0)= f(1) means that . f(0)= f(-1) means that .Find a basis for the space of all polynomials of degree at most 5 for which .

With those two equations you should be able to write two of the coefficients in terms of the other four. Now choose one of those four to be 1, the others 0, etc.