what to do for this one:

Given: 3 vectors,a,b,c, are linearly independent in a vector space V

Asked: Show that 3a, 2a-b,a+care also linearly independent

Results 1 to 3 of 3

- October 22nd 2009, 05:15 PM #1

- Joined
- Sep 2009
- Posts
- 158

- October 22nd 2009, 05:29 PM #2

- Joined
- Aug 2009
- From
- Israel
- Posts
- 976

Assume 3a, 2a-b, a+c are dependent. Then, there exist scalras , not all zero, such that

If then . Therefore not all the coefficients are zero.

Let

Then but not all of the coefficients are zero, in contradiction to the fact that a,b,c are linearly independent... ==> the assumption can not hold, therefore 3a, 2a-b and a+c are linearly independent.

- October 22nd 2009, 05:51 PM #3

- Joined
- Sep 2009
- Posts
- 158