Homework Help: Linear algebra - basis of subspace

1. Nov 12, 2009

cdub2

1. The problem statement, all variables and given/known data

Find a basis of the subspace of R4 that consists of all vectors perpendicular to both

(1
0
5
2)

and

(0
1
5
5)

^ those are vectors.

2. Relevant equations

3. The attempt at a solution

I understand that a basis needs to be linearly independent and that it needs to span the vector space, but I am thrown off by the fact that the basis needs to consist of vectors perpendicular to those vectors above.

2. Nov 12, 2009

crappyjones

do you know about orthogonal projections? or perhaps the gram-schmidt process? seems like the perfect time to use it. dont know if wikipedia links are allowed to be posted here, but here is a link to gram schmidt in case you havent read about it. the process itself might seem tedious but is very simple.

http://en.wikipedia.org/wiki/Gram–Schmidt_process

hope this helps.

cj.

3. Nov 12, 2009

Staff: Mentor

Another approach is to Let u = (u1, u2, u3, u4) be a vector in R4.

Since u is perpendicular to both of your given vectors, the dot product of u with each of the given vectors should be 0. That will give you two equations in four unknowns. These equations can be used to find a basis for your subspace.

Last edited: Nov 12, 2009
4. Nov 12, 2009

cdub2

thanks! i got it :)