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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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 f(u1), f(u2),…, f(un) are linearly independent then u1, u2,…, un are linearly independent
2) If f(u1), f(u2),…, f(un) are generators then u1, u2,…, u n are generators
3) If u1,u2,…,un are orthogonal two by two then f(u1), f(u2),…, f(un) are orthogonal