Find a basis for the orthogonal complement of the row space of A:
[1 0 2
1 1 4]
Split x = (3,3,3) into a row space component xr and a nullspace component xn.
The Attempt at a Solution
For the first part of the problem I took A to RREF
[1 0 2
0 1 2]
and then solved to find a basis for the nullspace, x * (-2,-2,1), which should be the basis for the orthogonal complement of the row space.
I THINK that's right but maybe it's not because I'm stuck on the second part, splitting x = (3,3,3). Do I try to find a vector in Row(A) and a vector in Nul(A) that, when added, produce the vector (3,3,3)? How do I solve for that?
Help is very much appreciated!
Also, what's the best way to represent a matrix on these message boards?