Question: Let V be a vector space with dimension n. Consider the following statements. (i) Every independent set in V is a basis for V

Let V be a vector space with dimension n. Consider the following

Let V be a vector space with dimension n. Consider the following statements. (i) Every independent set in V is a basis for V (ii) Every set in V that spans V must be independent (iii) Every set in V with less than n vectors must be independent. Which of the above statements is always true? (a) (ii) and (iii) only (b) (iii) only (c) (ii) only (d) none of them (e) (i) only

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