In each case, either prove the assertion or give an example showing that it is false. (a)
Question:
(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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a No If P 3 spanf 1 x f 2 x f 3 x f 4 x where f i 0 0 for each i then each polynomial px in P 3 ...View the full answer
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