Given the following statements determine if they are true or false. For those that are false, give an example that shows
Posted: Tue Sep 07, 2021 7:46 am
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
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