I'm not sure whether I'm correct or not.
My approach is -
As Ax = 0 and Ay = 0 , so x and y are null space of A. So dimension of NullSpace = 2
now -
Dimension of Matrix(3) = Rank + Dimension of NullSpace(2)
so, Rank = 3 - 2 = 1
Now Range of a matrix means Column Space of Matrix.
So Dimension of Column Space of Matrix = Rank of Matrix = 1
So in my opinion 1 is the answer.
Please tell the correct answer.