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Question: consider the vector space a show that w is a...

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Consider the vector space (a) Show that W is a subspace of R3 (the vector space of polynomials of degree at most 3) (b) Find a basis for W HINT for (b): i.) Plug in 1 and 2 to get equations for a, b, c, d from p(1) 0 and p(2) 0. ii.) Write these equations as for some matrix A. ii.)To solve these equations, use row reduction and the padding trick to find the null space of A. iV.) Each column where you added a -1 is a solution for (a, b, c, d). Plug these values of a, b, c, d back into p() so that each of these columns corresponds to a polynomial. These polynomials form a basis for W.

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