[Question] Let p1, p2 and p3 be 3 distinct points in PC2( Projective space, ie (z0,z1,z2) belong to PC2) Find the dimension of the linear system of cubics containing these 3 points. I have solved it for the non collinear case, by taking a projective transformation of the 3 points to [1,0,0],[0,1,0] and [0,0,1] respectively. And substituting those values into the equation of a cubic, to get that there are 6 coefficients remaining, therefore the dimension of the linear system is 6 by definition. But I am stuck on the collinear case (or maybe it can be shown generally?), thanks in advance for any help that can be given.