[java] Possible non array matrix

I'm thinking about making a few matrix classes in Java. The thing I was contemplating was making the matrix representation nothing but public member variables in the class. So for instance:

public Matrix4D
{
   public float m11, m12, m13, m21, m22, m23, m31, m32, m33;
}//  And that's pretty much all she wrote

public Matrix3D
{
   public float m11, m12, m21, m22, m31, m32;
}

I don't know if the AffineTransformation already implements a matrix this way, I'm geussing it doesn't, for 2 reasons. 1 being that it might assume the last column to be [0 0 0 1]' And it might use an array for the variable storage. I have to admit that I haven't done too much 2D or 3D programming, so I can't think of a reason right now not to do it the way I just mentioned. But I'm writing this to get some one else's ideas and comment, if they have experience programming 2D and 3D stuff. Thanks, L-