\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that for \(A \in M_{n,p}(\mathbb{K})\), the solution set of the homogeneous system \(A Y = 0\) is closed under linear combinations: if \(Y_1, Y_2\) are solutions and \(\lambda_1, \lambda_2 \in \mathbb{K}\), then \(\lambda_1 Y_1 + \lambda_2 Y_2\) is also a solution.
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