(a) Prove that for every positive integer n, one can find n + 1 linearly independent
Chapter 4, Problem 21(choose chapter or problem)
(a) Prove that for every positive integer n, one can find n + 1 linearly independent vectors in F (, ). [Hint: Look for polynomials.] (b) Use the result in part (a) to prove thatF (, )is infinitedimensional. (c) Prove that C(, ), Cm(, ), and C(, ) are infinite-dimensional. 22. Let S
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