I have two matrices $X_1$ and $X_2$ both with dimension $n \times p$, $\boldsymbol{\beta}_1$ and $\boldsymbol{\beta}_2$ are $p-$dimensional vectors finally, $f(\cdot)$ is a monotone positive function.
\begin{equation} \boldsymbol{\mu} = \begin{pmatrix} X_1 \boldsymbol{\beta}_1\\ f(X_2\boldsymbol{\beta}_2) \end{pmatrix} \end{equation}
I'd like to rewrite $\boldsymbol{\mu}$ separating $X_1$ and $X_2$ in a matrix, $\boldsymbol{\beta}_1$ and $\boldsymbol{\beta}_2$ in other. For example, if $f(\cdot)$ is identity, that is, $f(x) = x$ the desired result is
\begin{equation} \boldsymbol{\mu} = \begin{pmatrix} \boldsymbol{X}_1 & 0 \\ 0 & \boldsymbol{X}_2 \end{pmatrix} \begin{pmatrix} \boldsymbol{\beta}_1\\ \boldsymbol{\beta}_2 \end{pmatrix} \end{equation}