Let \(V \subset \mathbb{R}^{11}\) be a linear subspace of dimension 4 and consider the family \(\mathcal{A}\) of all linear maps \(L: \mathbb{R}^{11}->\mathbb{R}^{9}\) each of whose nullspace contain \(V\).
Show that \(\mathcal{A}\) is a linear space and compute its dimension.