Question

Let $S_1$ and $S_2$ be two subsets of $\mathbb{R}^3$ defined as $S_1 = \{(x, y, z) \in \mathbb{R}^3 : x + y = 2z\}$ $S_2 = \{(x, y, z) \in \mathbb{R}^3 : x = 2y, y - 2z = 0\}$. Then (1) only $S_1$ is a subspace of $\mathbb{R}^3$. (2) only $S_2$ is a subspace of $\mathbb{R}^3$ (3) $S_1$ and $S_2$ both are subspaces of $\mathbb{R}^3$. (4) None of the given answers is true.

          Let $S_1$ and $S_2$ be two subsets of $\mathbb{R}^3$ defined as
$S_1 = \{(x, y, z) \in \mathbb{R}^3 : x + y = 2z\}$
$S_2 = \{(x, y, z) \in \mathbb{R}^3 : x = 2y, y - 2z = 0\}$. Then
(1) only $S_1$ is a subspace of $\mathbb{R}^3$.
(2) only $S_2$ is a subspace of $\mathbb{R}^3$
(3) $S_1$ and $S_2$ both are subspaces of $\mathbb{R}^3$.
(4) None of the given answers is true.

$Let S1 and S2 be two subsets of ℝ^3 defined as S1 = {(x, y, z) ∈ℝ^3 : x + y = 2z} S2 = {(x, y, z) ∈ℝ^3 : x = 2y, y - 2z = 0}. Then (1) only S1 is a subspace of ℝ^3. (2) only S2 is a subspace of ℝ^3 (3) S1 and S2 both are subspaces of ℝ^3. (4) None of the given answers is true.$

Added by Valerie A.

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