Determine whether the following sets are subspaces of R3 under the operations of additio...

Determine whether the following sets are subspaces of R³ under the operations of addition and scalar multiplication defined on R³. Justify your answers.

(a) W₁ = {(a₁, a₂, a₃) ∈ R₃ : a₁ = 3a₂ and a₃ = −a₂}

(b) W₂ = {(a₁, a₂, a₃) ∈ R3 : a₁ = a₃ + 2}

(c) W₃ = {(a₁, a₂, a₃) ∈ R₃ : 2a₁ − 7a₂ + a₃ = 0}

(d) W₄ = {(a₁, a₂, a₃) ∈ R₃ : a₁ − 4a₂ − a₃ = 0}

(e) W₅ = {(a₁, a₂, a₃) ∈ R₃ : a₁ + 2a₂ − 3a₃ = 1}

(f) W₆ = {(a₁, a₂, a₃) ∈ R₃ : 5a²₁ − 3a²₂ + 6a²₃ = 0}