Let A Rmn and let be a solution to the least squares problem Ax =

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Let A ∈ Rm×n and let  be a solution to the least squares problem Ax = b. Show that a vector y ∈ Rn will also be a solution if and only if y =  + z, for some vector z ∈ N(A). [N(ATA) = N(A).]
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