This is a two part question:
a) Let S= (v1,v2,v3) , where:
v1 = (1,2,3) v2 = (2,1,4) v3 = (1,1,2)
Find a basis for the subspace V= span S of R^3.
I thought I understood how to do this but now I think I'm weong because the second part doesn't apply to my answer. I expressed the vectors as the columns of a matrix and found the basis of the column space to be all 3 vectors which are then the basis for span S. But the second part states:
b) Express each vector not in the basis as a linear combination of the found basis vector.
With my answer all 3 vectors are in the basis so where did I go wrong?
Any help would be appreciated.
Thanks in advance.