- #1
Geekster
- 38
- 0
I have the set
[tex]
s = span ( [[0][1][-1][1]]^{T} )
[/tex]
And I need to find the orthogonal complement of the set.
It seems like it should be straight foward, but I'm a bit confused. I know that S is a subspace of R^4, and that there should be three free vairables.
What I did so far is to take the column vector given, and I need to find the null space of its transpose. The three free variables I picked are [tex]x_1= s, x_2=t, x_3=w, x_4=t-w[/tex].
However, x_1=s is throwing me off because its always zero. I guess what I'm really asking is, what exactly is the solution space of the homogenous system,
[tex]
Ax=0
[/tex]
in this problem?
Thanks
[tex]
s = span ( [[0][1][-1][1]]^{T} )
[/tex]
And I need to find the orthogonal complement of the set.
It seems like it should be straight foward, but I'm a bit confused. I know that S is a subspace of R^4, and that there should be three free vairables.
What I did so far is to take the column vector given, and I need to find the null space of its transpose. The three free variables I picked are [tex]x_1= s, x_2=t, x_3=w, x_4=t-w[/tex].
However, x_1=s is throwing me off because its always zero. I guess what I'm really asking is, what exactly is the solution space of the homogenous system,
[tex]
Ax=0
[/tex]
in this problem?
Thanks
Last edited: