Find the Orthogonal Complement

[Tempest Desh]

Homework Statement

Find the orthogonal complement.

Homework Equations

span {[0 0 1 0] [2 -1 0 1]} transpose

The Attempt at a Solution

I'm really confused on this. I've tried setting up things like this:

[0 0 1 0] [2 -1 0 1] [x y z v] transpose = [0 0 0 0] transpose

But, I'm not sure where to go from here...all the examples I see having two column matrices...not split up like in this problem...

 

[Mark44]

Homework Statement

Find the orthogonal complement.

Homework Equations

span {[0 0 1 0] [2 -1 0 1]} transpose

The Attempt at a Solution

I'm really confused on this. I've tried setting up things like this:

[0 0 1 0] [2 -1 0 1] [x y z v] transpose = [0 0 0 0] transpose

But, I'm not sure where to go from here...all the examples I see having two column matrices...not split up like in this problem...

Any vector <x, y, z, v> in the orth. complement has to be orthogonal to (perpendicular to) each of the two vectors in your set. The dot product of each of your two given vectors with <x, y, z, v> will be zero. That will give you two equations in four unknowns, from which you can find two vectors that form a basis for the orthogonal complement.