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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.
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