Prove that if L and P are three dimentional subspaces of R5, then L and P must have a nonzero constant in common.

i am just stuck now on how to get this proof started... any thoughts on how to start?

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- May 1st 2009, 10:07 AMshuaigesubspace proof
Prove that if L and P are three dimentional subspaces of R5, then L and P must have a nonzero constant in common.

i am just stuck now on how to get this proof started... any thoughts on how to start? - May 1st 2009, 10:46 AMHallsofIvy
What does it mean to say a subspace has a "non-zero constant"?

Do you mean to say the L and P have a non-zero vector in common? That is, that there exist at least one non-zero vector in both P and Q.

If so, construct a basis for each of P and Q. If L and P have no non-zero vectors in common, then the union of the two bases is still independent and so span a subspace of dimension 6, which is impossible. - May 1st 2009, 11:18 AMshuaige
i guess it means non zero vectors, but what my instructor gave us is "non zero constant"

i am kinda confused on this too.

thanks for ur reply