Consider the vector space V = P?(?) and the set S ? P?(?) given by:
S = {1 + x, 1 - x, 2 - x², x²}
Now do the following:
• Show that S is NOT a basis of V = P?(?). Make sure to explain your reasoning clearly.
• Create a basis by getting rid of at least one vector from S. Show that your new set is a basis.
Make sure your work on both parts is clear, complete, and detailed. Do not use determinants. If a matrix pops up
without clear explanation, I will deduct many points.