I have v1 = [ [1,2] [-2,1]] and v2 = [[3,2][-1,1]] and I want to know if various "w"s are linear combinations. How do I set this up?

I think there should be some form of:

[ [1, -2, 3, -1] [2, 1, 2, 1] | [w]] and then get it into rho echelon form to understand whether they are linear combinations or not. Is this true?

example w = [[1,0][0,1]]

10/2/2006 12:33:14 AM

melih

10/2/2006 10:55:22 AM

I don't really understand/remember that notation you are using, but you've got the right idea. Given two vectors a1 and a2, to see if "w" is a linear combination of a1 and a2, solve the system Ax=w where A consists of a1 for first column and a2 for second column. This is equivalent to a1(x1) + a2(x2) = w.

10/2/2006 9:16:03 PM