SOLUTION: Let V be a vector space with dimension 11 and S be a subset of V which is linearly independent and has 10 vectors. Consider the following statements: (a) Every non-empty subset of

Question 1174474: Let V be a vector space with dimension 11 and S be a subset of V which is linearly independent and has 10 vectors. Consider the following statements:
(a) Every non-empty subset of S is linearly independent.
(b) S is a basis of V.
(c) There exists a subset S1 of S which is linearly dependent.
(d) Dimension of span(S) < dimension of V.
Which of the above statements is/are False?

Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.

(b)   is False.

The rest of statements a), c), and d) are   TRUE.

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