Check whether the following sets are vector subspaces of the vector space ℝ³:

1. E₁ = {(x, y, z) ∈ ℝ³ | x + y + z = 0}
2. E₂ = {(x, y, z) ∈ ℝ³ | y − 3x = 0 and z = 0}
3. E₃ = {(x, 2x, x) | x ∈ ℝ}
4. E₄ = {(x, y, z) ∈ ℝ³ | x² − z² = 0}

Let u₁ = (1, 2, 3, 4) and u₂ = (1, −2, 3, −4) be vectors in ℝ⁴. Can we determine the real numbers x and y for which:

1. (x, 1, 1, y) ∈ vect(u₁, u₂)?
2. (x, 1, 1, y) ∈ vect(u₁, u₂)?

Is vect(u₁, u₂) a vector subspace generated by u₁ and u₂?