Thread: Find a basis

I don't know why this one is giving me such a hard time but it is:

Find a basis for the set of vectors in R^3 in the plane x + 2y + z = 0



Thank you!

Hello

Originally Posted by baxyjr

I don't know why this one is giving me such a hard time but it is:

Find a basis for the set of vectors in R^3 in the plane x + 2y + z = 0

Any two vectors of the plane which don't share the same direction will give you a basis of this plane. To find two such vectors one can pick up three points , and on the plane and check that .

Originally Posted by flyingsquirrel

Hello

Any two vectors of the plane which don't share the same direction will give you a basis of this plane. To find two such vectors one can pick up three points , and on the plane and check that .

Thank you!

Ok, I think I get it.

So you're saying that as long as I pick two vectors in R3 that are linearly independent and satisfy the equation, that I am good?

Thank god for this site! Especially when you are taking a class that normally covers 4 months in four weeks!

Originally Posted by baxyjr

Thank you!

Ok, I think I get it.

So you're saying that as long as I pick two vectors in R3 that are linearly independent and satisfy the equation, that I am good?

Yes. The plane will be a vector space of dimension 2, so any two linearly independent vectors in it will form a basis.