Word Count : 281

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We are given the set: $$ W = \{(x, y, z) \in \mathbb{R}^3 \mid x + y - z = 0\} $$ We are to check numerically and manually whether $W$ is a subspace of $\mathbb{R}^3$. --- ### Step 1: Check if Zero Vector is in $W$ The zero vector in $\mathbb{R}^3$ is: $$ \mathbf{0} = _________ ______ ____ ______ __________ ______ _______ _______.
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