Find all subspaces of the real vector space $\Bbb R^2$. Is is true for any elements $u=(a, b)$ and $v=(c, d)$ of $\Bbb R^2$,there exists a non-trivial subspace $W$ of $\Bbb R^2$ such that $u, v \, € \, W$?
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2I will put as much effort in this comment as you did in your question: the answer is No. – Antoine Mar 25 '16 at 16:03
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What's a non-trivial subspace? Is $\mathbb{R}^2$ a "non-trivial subspace" of itself? – Ian Mar 25 '16 at 16:04
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All subspaces are $0,l_0, l_m, \mathbb {R^2}$ where $l_m=\{(x,xm): x\in\mathbb {R}\}$ for all $m\in\mathbb {R}$and $l_0 =\{(0,x): x\in\mathbb {R}\}$ .
The answer to your question is no, because, for example the subspace generated by $(1,1)$ and $(1,2)$ are all $\mathbb {R^2}$.
Martín Vacas Vignolo
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