(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is the following a subspace of [itex]R^{n}[/itex] for some n?

[itex]W = {(x, y, z) \in R^{3} | 2x - y = 3z + x = 0}[/itex]

2. Relevant equations

A subspace of [itex]R^{n}[/itex] is a subset [itex]W[/itex] of [itex]R^{n}[/itex] such that;

1. [itex]0 \in W[/itex]

2. [itex]\forall u, v \in W; u + v \in W[/itex]

3. [itex]\forall c \in R[/itex] and [itex]u \in W[/itex]; [itex]cu \in W[/itex]

3. The attempt at a solution

I have checked that the zero vector is contained in the subset, by first letting x = 0.

2x - y = 0, therefore if x = 0, y is also equal to 0.

3z + x = 0, so if x = 0, z is also equal to 0.

The problem here is that now I have no idea how to prove that W is closed under addition and scalar multiplication.

Any help would be greatly appreciated! :)

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# Proving if a subset is a subspace

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