In the following, find out whether S froms a subspace of V ?

(a) V = R3, S = {(x1, x2, x3) : x1 + 5x2 + 3x3 = 0}

(b) V = R3, S = {(x1, x2, x3) : x1 + 5x2 + 3x3 = 1}

(c) V = R3, S = {(x1, x2) : x1 ≥ 0, x2 ≥ 0}

(d) V = P(R), the set of all polynomials over reals and S = {p(x) ∈ P(R) : P(5) = 0}

(e) V = Rn, S = {(x1, x2, ..., xn) : x1 = x2}

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