Given is a basis for .
a) For which values of k are vectors 1) independent 2) dependent
b) In cases where are dependent, write as a linear combination of and
c) For which values of k does the group span
a) I proved that when k does not equal 2, they are independent. And when k = 2 they are dependent.
b) i proved that
c) and this is where i am having trouble. I came to the conclusion that the group spans as long as and both are not linear combination of . (It doesn't matter if one of the two is a linear combination since there are 5 vectors) It is given that is a basis for . That means that are independent of each other. By doing the work, I got that and are both not linear combinations of which means it doesn't matter what value is. Can someone please help me with this. Thank you very much