Question

How do you show that a set of vectors from the basis of R^3?

Answer 1

The questions specifically asks about v1=[-1, 0, 3] v2 = [-1, 1, 0] and v3= [0, 1, 2]

Answer 2

I know that it must be a spanning set and linearly independent and I know how to show it is linearly independent, I just don't know how to show it is a spanning set.

Answer 3

aahh

Answer 4

Sorry, that is above my head, we haven't done determinants

Answer 5

Take any point in R3 say (15, 14,-3)

k1v1+k2v2+k3v3 = (15,14,-3)
k1[-1, 0, 3]+ k2[-1, 1, 0] + k3[0, 1, 2]
(-k1-k2,k2+k3,3k1+ 2k3) = ( 15,14,-3)

solve for k1 k2 k3 you must get them

Answer 6

OK I think I get that

Answer 7

k1 k2 k3 are scalars ?