Proving S is a Subset of T in R³

[umzung]

Homework Statement

Show that S ⊆ T, where S and T are both subsets of R^3.

Homework Equations

S = {(1, 2, 1), (1, 1, 2)},
T ={(x,y,3x−y): x,y∈R}

The Attempt at a Solution

I considered finding if S is a spanning set for T but I'm aware that this is perhaps not relevant. If I find {α(1, 2, 1) + β(1, 1, 2): α, β ∈ R}, would this show S to be a subset of T?

 

[BvU]

Hello Unzung,

I'm aware that this is perhaps not relevant

You are right there !

You are done once you have shown that each element of S is also a member of T.