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Prove that the set W is a subspace of

5.A] Prove that the set $W = {(x, y, z) \in \mathbb{R}^3 \mid x - 3y + 4z = 0}$ is a subspace of $\mathbb{R}^3$ .

Answer:

Prove that the set <span class="wp-katex-eq" data-display="false"> W = {(x, y, z) \in \mathbb{R}^3 \mid x - 3y + 4z = 0} </span> is a subspace of <span class="wp-katex-eq" data-display="false"> \mathbb{R}^3 </span>.

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