If are linearly independent vectors in , show that is linearly independent set.
If where , since is linearly independent.
Is the proof correct? I felt something missing in the proof.
If are linearly dependent vectors in , show that is linearly dependent set for any .
If . Since are linearly dependent, for some . Thus, is linearly dependent.
Please check my proofs.
Let and , is invertible .
Show that are linearly independent if and only if are linearly independent vectors in .
How to prove problem 3? what theorem do I need?