load("linearalgebra");

m : matrix([1,2],[1,2]);

nullspace(m);

columnspace(m);

ptriangularize(m-z*ident(2),z);

m : matrix([1,2,3],[4,5,6],[7,8,9]) - z * ident(3);

mm : ptriangularize(m,z);

algebraic : true;

tellrat(mm[3,3]);

mm : ratsimp(mm);

nullspace(mm);

m : matrix([1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]);

column_space(m);

apply('orthogonal_complement, args(nullspace(transpose(m))));

untellrat(z);