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Why is the subspace associated with the affine set for a set of linear equations the null space?
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I'm reading my optimization textbook, and it's going over affine sets. It gives an example where it proves that the solution set of a system of lienar equations is an affine set. After doing so, it says that the "subspace associated with the affine set is the nullspace".
My question is: why is the nullspace the set associated with it? How do they know they? And why does that matter?
Here's a link to the full question: https://imgur.com/gallery/affine-sets-linear-equations-N2eUHuc
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