Let W= (x, y, z) Prove that W is a subspace of ∈ℝ How can I resolve this ?

Question

Let W= x=1 Prove that W is a subspace of ∈ℝ
How can I resolve this ?

Answer 1

W is not a subspace.

Explanation:

Notice that (-1,2,2) and (-1,5,3) are both elements of W. Because its x coordinate, x = -1, satisfy the condition |x| = 1.

but (-1,2,2) + (-1,5,3) = (-2,7,5) do not belongs to W. Because its first coordinate, x =-2, do not satisfy |x| = 1.