Find a basis for the subspace of R 3 that is spanned by the

Find a basis for the subspace of R ^3
that is spanned by the vectors v1 = (1, 0, 0),
v2 = (1, 0, 1), v3 = (2, 0, 1), v4 = (0, 0, 1).

Solution

v1-v2=v4

v1+v2=v3

So v1,v2 span the subspace spanned by given 4 vectors

Let, av1+bv2=0

So, a+b=0

b=0

HEnce, a=0

HEnce,v1,v2 are linearly independent

So, v1,v2 form basis for this subsapce