# Possible subspaces

Algebra Level 4

Let $$V$$ be the vector space $$\mathbb{C}^2$$, or the set of vectors with two complex number components. Which of the following, if any, are subspaces of $$V$$?

1. The set of vectors $$\begin{pmatrix}x\\y\end{pmatrix}$$ for which $$xy = 0$$.
2. The set of vectors $$\begin{pmatrix}x\\y\end{pmatrix}$$ for which $$x$$ and $$y$$ are both integers.
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