![m := matrix([[1, 3, 4], [-1, 2, 4], [5, 2, 1]])](images/smith1.gif)
We calculate the Smith Normal Form of the matrix M by row and column operations.
> m:=matrix(3,3,[[1,3,4],[-1,2,4],[5,2,1]]);
> det(m);
> m:=addrow(m,3,2,-4);
![m := matrix([[1, 3, 4], [-21, -6, 0], [5, 2, 1]])](images/smith3.gif)
> m:=addrow(m,3,1,-4);
![m := matrix([[-19, -5, 0], [-21, -6, 0], [5, 2, 1]]...](images/smith4.gif)
> m:=addcol(m,3,2,-2);
![m := matrix([[-19, -5, 0], [-21, -6, 0], [5, 0, 1]]...](images/smith5.gif)
> m:=addcol(m,3,1,-5);
![m := matrix([[-19, -5, 0], [-21, -6, 0], [0, 0, 1]]...](images/smith6.gif)
> m:=addrow(m,2,1,-1);
![m := matrix([[2, 1, 0], [-21, -6, 0], [0, 0, 1]])](images/smith7.gif)
> m:=addrow(m,1,2,6);
![m := matrix([[2, 1, 0], [-9, 0, 0], [0, 0, 1]])](images/smith8.gif)
> m:=swaprow(m,1,2);
![m := matrix([[-9, 0, 0], [2, 1, 0], [0, 0, 1]])](images/smith9.gif)
> m:=addcol(m,2,1,-2);
![m := matrix([[-9, 0, 0], [0, 1, 0], [0, 0, 1]])](images/smith10.gif)
Now change the sign on -9 and move it to the bottom corner for strict SNF.
>