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 7:47 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 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
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