Given the following statements determine if they are true or false. For those that are false, give an example that shows their falsehood (counterexample); for them to be true, make the proof or quote it that sustains its validity.
Let E be a vector space and f a linear map from E to E
1) If u1, u2,…, un are linearly independent then f (u1), f (u2),…, f (un) are linearly independent
2) If u1, u2,…, un are generators then f (u1), f (u2),…, f (un) are generators
Given the following statements determine if they are true or false. For those that are false, give an example that shows
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