Prove that if V and W are the three dimensional subspaces of R5 then V and W must have a nonzero vector in common.
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Step 1: Since V and W are three-dimensional subspaces of R^5, they each have a basis with three linearly independent vectors. Show more…
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Prove that if $\mathbf{V}$ and $\mathbf{W}$ are three-dimensional subspaces of $\mathbf{R}^{5}$, then $\mathbf{V}$ and $\mathbf{W}$ must have a nonzero vector in common. Hint: Start with bases for the two subspaces, making six vectors in all.
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