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Determine whether $\{(x_1,x_2,x_3)^T \mid x_1 = x_2 = x_3\}$ is a subspace

I know that I must show that it is closed under addition and multiplication, but I'm confused as to how I should approach doing that.

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    Just write down and unfold the definition of "closed under addition" and similarly for multiplication. There is almost nothing that needs to be done.2012-09-27
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    This is the span of $\{(1,1,1)\}$. If you know that the linear span of any nonempty set is a subspace, you are done.2012-09-27

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