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
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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