Question

Find b and c if the set V ={(1,1,0) + k(3,b,c) : k in R } is a subspace of R3.

Answer 1

@wio

Answer 2

By subspace, does that mean it shouldn't span all of \(\mathbb R^3\)?

Answer 3

I think so. but it has 2 dimensions, right?

Answer 4

do we have to find linear transformation T : R^3 to R^2?

Answer 5

Yeah, but even if you did something like \(b=3,c=0\), giving only one linearly independent vector, it is still a subspace. So I'm wondering what I'm missing that makes this problem nontrivial.

Answer 6

I hand off. go to bed now. Thanks for reply.