Question

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.]

Answer 1

Do you have any clue how to start this?

Answer 2

nope

Answer 3

Well, a two-dimensional subspace of \(\mathbb{R}^3\) is a plane, right?

Answer 4

um not always, you could have a two dim subspace with 2 linear independent vectors and span a line

Answer 5

but either way, this is not the important part of the question.

Answer 6

That's right; you could span two lines that intersect at the origin.