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Is it possible to find a pair of two -dimensional sub-spaces U and V of R^3 such that U intersection V = {0}? Prove your answer. Give a geometricle interpretation of your conclusion. [ hint: let {u_1,u_2} and {v_1,v_2} be bases for U and V, respectively. Show that u_1,u_2,v_1,v_2 are linearly independent.]

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Do you have any clue how to start this?
Well, a two-dimensional subspace of \(\mathbb{R}^3\) is a plane, right?

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Other answers:

um not always, you could have a two dim subspace with 2 linear independent vectors and span a line
but either way, this is not the important part of the question.
That's right; you could span two lines that intersect at the origin.

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