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Show that \(\mathcal{A}\) is a linear space and compute its dimension.

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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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