There is a subspace that contains all the vectors in the form (x, 2y, x). Decompose the vector (2, 3, -1) into a sum of an element from the orthogonal complement of this subspace and an element from the subspace. Find the distance from (2, 3, -1) to this subspace.
The Attempt at a Solution
To find the orthogonal complement of this subspace, I found the kernel, which in this case happens to only contain the zero vector. That means only a particular solution exists, but obviously (2, 3, -1) is not a particular solution, so I'm not sure how to decompose this, much less find the distance.