use of SVD

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My data are 9 points (0,0,1) (1,0,3) (2,0,5) (0,1,4) , (1,1,8) (2,1,7) (0,2,7) (1,2,8) (2,2,8)

I want to solve z = M p where p=[ a b c] and a xi+ byi +c =zi

Mat z=(Mat_<double>(9,1) << 1, 3, 5, 4, 8, 7, 7, 8, 8);
Mat m=(Mat_<double>(9,3) << 0, 0 ,1/**/,1,0 ,1/**/,2 ,0 ,1/**/,0 ,1 ,1/**/,1 ,1, 1/**/, 2, 1, 1/**/, 0,2, 1/**/, 1,2,1/**/, 2, 2, 1);
SVD s(m);
Mat dst;
Mat singularValue;
s.backSubst(z,dst);
cout<<"Solution z= m dst"<< dst<<endl;
s.compute(m,singularValue);
cout<<"singular value :"<<singularValue<<endl;
Mat mp=(Mat_<double>(9,4) << 0, 0 ,1,1/**/,1,0 ,3,1/**/,2 ,0 ,5,1/**/,0 ,1 ,4,1/**/,1 ,1, 8,1/**/,2, 1, 7,1/**/, 0, 2, 7,1/**/, 1,2,8,1/**/, 2, 2, 8,1);
SVD s2(mp);
Mat a;
s2.solveZ(mp,a);
cout<<"Solution mp *a =0"<<a<<endl;

and it gives answer :

Solution z= m dst[1.333333333333331;
 2.333333333333332;
 2.000000000000002]
singular value :[5.592252381884617;
 2.449489742783178;
 1.314044632919994]
Solution mp *a =0[0.3330915074747192;
 0.6439188217126393;
 -0.2753503146060172;
 0.6313484005989033]

I hope it will help you