Determine whether each of the following is a subspace or not. Justify your answer! {(x, y,...

 

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Determine whether each of the following is a subspace or not. Justify your answer! {(x, y, z) = R³ | 2x − 3y + 4z = 0} - (i) W₁ := 1 E (ii) W₂ := {A € R³×³ | adj(A) = AT }, where adj(A) denotes the adjoint matrix, and AT denotes the transpose of A € R³×³. (iii) W3 := {p(x) = P3 | P(0) ≤ 2} Determine whether each of the following is a subspace or not. Justify your answer! {(x, y, z) = R³ | 2x − 3y + 4z = 0} - (i) W₁ := 1 E (ii) W₂ := {A € R³×³ | adj(A) = AT }, where adj(A) denotes the adjoint matrix, and AT denotes the transpose of A € R³×³. (iii) W3 := {p(x) = P3 | P(0) ≤ 2}