【归档】给出R^2的一个非空子集U的例子，使得U在标量乘法下是封闭的，但U不是R^2的子空间

Note: 旧的wordpress博客弃用，于是将以前的笔记搬运回来。

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Question:
Give an example of a non-empty subset $U$ in $R^2$ such that $U$ is closed under scalar multiplication, but $U$ is not a linear subspace of $R^2$.

Solution:
Let $U$ = { $(x,y)|x=0ory=0$}.
Now we take $u\in U,a\in \mathbb{R}$