Solved: Use Exercise 27 to show that if and are bases for
Chapter 2, Problem 28E(choose chapter or problem)
Use Exercise 27 to show that if and are bases for a subspace W of , then cannot contain more vectors than , and, conversely, cannot contain more vectors than .Exercise 27:Suppose vectors span a subspace W, and let be any set in W containing more than p vectors. Fill in the details of the following argument to show that a. Explain why for each vector aj , there exists a vector cj in such that .b. Let . Explain why there is a nonzero vector u such thatc. Use B and C to show that Au = 0: This shows that the columns of A are linearly dependent.
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