AT y d is solvable when d is in which of the four subspaces

A^T y = d is solvable when d is in which of the four subspaces? The solution y is unique when the contains only the zero vector.

Solution

A^Ty=d is solvable when d is in the row space, which consists of all vectors A^Ty.

The solution y is unique when the left nullspace contains only the zero vector.