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I'm stuck with the following problem and I've tried approaching it by extending the initial base of $W$ without luck. Any hints??
Consider two subspaces $W_1$ and $W_2$ of the vector space $\mathbb R^2$ such that dim $W_1=\dim W_2=1$. Prove that there exists a subspace $W$ such that $V=W \bigoplus W_1$ and $V=W \bigoplus W_2$.

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    What is $V$? $\Bbb R^2$?2012-01-26
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    the problem doesn't specify but I assumed so2012-01-26
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    Think about what these spaces really are (as familiar geometric objects). $W_1$ is a line through the origin. $W_2$ is also a line through the origin, maybe the same line as $W_1$, maybe not. Given any two directions in the plane, so long as they aren't parallel or opposite, you can get anywhere in the plane in exactly one way by going an appropriate distance in the first direction, followed by an appropriate distance in the second.2012-01-27
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    Yes I think I should have thought of it that way first instead of rushing to have an algebraic solution.2012-01-27

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