Prove Theorem 7.16: Let V = {v1, ... , vm} be a subset of avector space V with dim(V) =

Chapter 7, Problem 57

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Prove Theorem 7.16: Let V = {v1, ... , vm} be a subset of avector space V with dim(V) = n.(a) Prove that if m < n, then V does not span V.(b) Prove that if m > n, then V is linearly dependent.58. Prove Theorem 7.17: Let V = {v1, ... , vm} be a subset of avector space V with dim(V) = m. If V is linearly independent orspans V, then V is a basis for V.

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