@Carl Love 

Yes, I am looking for the basis of the intersectio between these two subspaces. Once I have the intersection between both subspace, then I need the complementay betweeh one of the original basis and the intersection between both basis. I assume that the intersection is maple in the intersection between the sets, but not between the spaces :-( Actually, what I really need is the complementary to the intersection, but "minus" does not work. Sorry, too many years usign MATLAB! 

Here is the code:

with(LinearAlgebra);

with(DEtools);

with(DynamicSystems);

A1 := Matrix(4, 4, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 2, (1, 4) = 0, (2, 1) = 3, (2, 2) = 4, (2, 3) = 5, (2, 4) = 6, (3, 1) = 0, (3, 2) = 0, (3, 3) = 7, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 8, (4, 4) = 9});

B1 := Vector(4, {(1) = 1, (2) = 2, (3) = 0, (4) = 0}); C1 := Vector[row](4, {(1) = 1, (2) = 0, (3) = 2, (4) = 0});

sys1 := StateSpace(A1, B1, C1, Matrix([0]));

CM := ControllabilityMatrix(sys1);

OM := ObservabilityMatrix(sys1);

X1 := ColumnSpace(CM);

X2 := SumBasis([X1[1], X1[2]]);

X3 := NullSpace(OM);

X4 := IntersectionBasis([X2, X3]);

`minus`(X2, X4)