My question is as follows. Assume the equation, $$P=\begin{bmatrix}V_1R_1 + V_2R_3 \\V_1R_3 + V_2R_2 \end{bmatrix},$$ where $V_1,V_2\in\mathbb{R}^{1\times \nu}$, $R_1,R_2,R_3 \in \mathbb{R}^{\nu \times \nu}$ and the following equality $$ \Pi = \begin{bmatrix} V_1 \\ V_2 \end{bmatrix},$$ holds.
I would like to write $P$ as a matrix product involving $\Pi$ explicitly, say $M_1 \Pi M_2$ where $M_1$ and $M_2$ are suitable matrices. Any hint? Thanks!!!