Question

2. Determine each of the following, justifying your answers. (a) Is $\{(x, y, z) \in \mathbb{R}^3: x + 14y + 4z = 0\}$ a subspace of $\mathbb{R}^3$? (b) Is $\{(x, y, z) \in \mathbb{R}^3: x + 14y + 4z = 28\}$ a subspace of $\mathbb{R}^3$? (c) Is $\{(x, y) \in \mathbb{R}^2: x^2 = y^2\}$ a subspace of $\mathbb{R}^2$? (d) Is $\{(a, b) \in \mathbb{F}_2: a \cdot a + b = 0\}$ a subspace of $\mathbb{F}_2^2$?

          2. Determine each of the following, justifying your answers.
(a) Is \(\{(x, y, z) \in \mathbb{R}^3: x + 14y + 4z = 0\}\) a subspace of \(\mathbb{R}^3\)?
(b) Is \(\{(x, y, z) \in \mathbb{R}^3: x + 14y + 4z = 28\}\) a subspace of \(\mathbb{R}^3\)?
(c) Is \(\{(x, y) \in \mathbb{R}^2: x^2 = y^2\}\) a subspace of \(\mathbb{R}^2\)?
(d) Is \(\{(a, b) \in \mathbb{F}_2: a \cdot a + b = 0\}\) a subspace of \(\mathbb{F}_2^2\)?

$2. Determine each of the following, justifying your answers. (a) Is {(x, y, z) ∈ℝ^3: x + 14y + 4z = 0} a subspace of ℝ^3? (b) Is {(x, y, z) ∈ℝ^3: x + 14y + 4z = 28} a subspace of ℝ^3? (c) Is {(x, y) ∈ℝ^2: x^2 = y^2} a subspace of ℝ^2? (d) Is {(a, b) ∈𝔽2: a · a + b = 0} a subspace of 𝔽2^2?$

Added by Teresa F.

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