Let \begin{align} \Omega=\begin{bmatrix} L_1 & \cdots & L_{n-1} \\ M_1 & \cdots & M_{n-1} \end{bmatrix}\end{align} be a matrix of linear forms on $\mathbb{P}^n$, i.e. homogeneous polynomials of degree $1$, such that for any $[\lambda, \mu] \in \mathbb{P}$, the linear forms $\lambda L_1 + \mu M_1,\dots,\lambda L_{n-1}+\mu M_{n-1}$ are linearly independent. For each $[\lambda, \mu]$, the equations $\lambda L_1 + \mu M_1=\dots=\lambda L_{n-1}+\mu M_{n-1}=0$ define a line $\ell_{\lambda,\mu}$ of $\mathbb{P}^n$. The union of all the lines as $[\lambda,\mu]$ varies is precisely the rank-1 locus variety of $\Omega$.

**Question:** Does there exist an open set $\mathcal{U}$ of hyperplanes of $\mathbb{P}^n$, such that every hyperplane $H \in \mathcal{U}$ does not contain any $\ell_{\lambda,\mu}$? (Here we parametrize the hyperplanes of $\mathbb{P}^n$ by elements of $\mathbb{P}^n$: each such element defines the normal to a hyperplane.) In other words, can we say that a general hyperplane $H$ of $\mathbb{P}^n$ does not contain any of the lines $\ell_{\lambda,\mu}$?