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3. For each of the following statements, either provide a short proof that it is true...

3. For each of the following statements, either provide a short proof that it is true (or appeal to the definition) or provide a counterexample showing that it is false.

(e) Any set containing the zero vector is linearly dependent.
(f) Subsets of linearly dependent sets are linearly dependent.
(g) Subsets of linearly independent sets are linearly independent.
(h) The rank of a matrix is equal to the number of its nonzero columns.

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