Row-column transformation dependence for two and three copies

Let $\upsilon,\upsilon_2,\upsilon_3,\ldots$ be the weighted-average ITV family defined in the source, and let the row-column-type transformations be the transformations on the transition parameters described there. The row-column dependence conjecture. Theorem holds for $N=2$ and $N=3$, namely, the row-column-type transformations are linearly dependent for these values of $N$. The source proves the corresponding dependence for $N\geq4$ under existence of the weighted-average ITV family and leaves the cases $N=2,3$ as a conjecture.