Linear algebra - basis of subspace

[cdub2]

Homework Statement

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.

Homework Equations

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.

 

[crappyjones]

do you know about orthogonal projections? or perhaps the gram-schmidt process? seems like the perfect time to use it. don't know if wikipedia links are allowed to be posted here, but here is a link to gram schmidt in case you haven't 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.

 

[Mark44]

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.

 

[cdub2]

thanks! i got it :)