Linear algebra: W-perp?
Consider R^4 together with the standard inner product and let W={(x1, x2, x3, x4) ϵ R^4 | x1+x2-x4=0}. Find a basis for W-perp.

How do you solve this question? All I can think of is that you have to put the elements in W in terms of others?

Question

Linear algebra: W-perp?
Consider R^4 together with the standard inner product and let W={(x1, x2, x3, x4) ϵ R^4 | x1+x2-x4=0}. Find a basis for W-perp. 

How do you solve this question? All I can think of is that you have to put the elements in W in terms of others?

da_scienceman · Answer

Tip for he66666: basis = Linearly set of vectors which span R^4

da_scienceman · Answer

U must check if the vectors are in d span of R^4, and are linearly independent................

he66666 · Answer

Yes, I am aware of that but even with that knowledge I don't know how to approach this question :/

da_scienceman · Answer

tip: span means I choose coeffs in a field say a1,a2...a4 and each vector in ur R^4 can be written as a linear combination; meanwhile, Linearly independent means I write all vectors as a linear combination such that all coeefficient taken from d field are zeroo
I can only give tips! @he66666

da_scienceman · Answer

I see x4 can be written as a combination of x1 and x2 so it tells me sthg is wrong with linearly independence! or NOT?

he66666 · Answer

Oh, I see! That cleared up things a bit. Thanks da_ScienceMan!

da_scienceman · Answer

sure mate!