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in general, you multiply a Mat by a row-vector, and receive a transformed col-vector.

vc = M * vr;

you could setup your Mat in the usual way, Mat m(4,4,CV32F); and assign one element after the other, but in this case you might want to profit from the ease of Mat_:

Mat m = (Mat_<float>(4,4) << 1,0,0,3,
                             0,1,0,3,
                             0,0,1,3,
                             0,0,0,1 );

// opencv can only multiply Mat's, so make one for the input vec (1,2,3):
Mat v = (Mat_<float>(4,1) << 1,2,3,1);  // note: 1 as last element
Mat r = m*v;
cerr << r << endl;

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