Question: In each case, either prove the assertion or give an example showing that it is false. (a) P2 has a basis of polynomials f(x) such

In each case, either prove the assertion or give an example showing that it is false.
(a) P2 has a basis of polynomials f(x) such that f(b) = 0.
(b) Every basis of M22 contains a noninvertible matrix.
(c) If {u, v, w} is independent then, au + bv + cw = 0 for some a, b, c.
(d) If {u, v} is independent, so is (u, u + v}.
(e) If {u, v, w} is independent, so is {u, v}.
(f) If {u, v, w} is independent, so is (u + v + w}.

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