Not sure if this functionality already exists, but you could try writing a custom function to do this perhaps.
Let’s say that the given matrix is called A. You figure out the eigenvalues of A and if the smallest (ordered by absolute values) is 0, then the corresponding (right) eigenvector is your desired vector. If not, you can calculate something like Gram-Schmidt process 2. Basically, start from some random vector and keep subtracting the component of each eigenvector from it iteratively. That should give you the vector that is perpendicular to all rows of A.
Hope this helps.