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5. Let S be the set of all polynomials p(x) of degree ≤ 4 such that...

5.
Let S be the set of all polynomials p(x) of degree ≤ 4 such that
p(-1)=0.
(a) Prove that S is a subspace of the vector space of all polynomials.
(b) Find a basis for S.
(c) What is the dimension of S?

6.
Let ? ⊆ R! be the span of ?1 = (2,1,0,-1), ?2 =(1,2,-6,1),
?3 = (1,0,2,-1) and ? ⊆ R! be the span of ?1 =(1,1,-2,0), ?2 =(3,1,2,-2). Prove that V=W.
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