Question: When X has less than full rank and we use a generalized inverse to estimate ????, explain why the space of possible least squares solutions

When X has less than full rank and we use a generalized inverse to estimate ????, explain why the space of possible least squares solutions ????̂

does not form a vector space. (For a solution, ????̂, this space is the set of

????̃ = ????̂ + ???? for all ???? ∈ N(X); such a shifted vector space is called an affine space.)

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