Another least squares example

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4.6.10. In many least squares applications, the underlying data matrix Am × n does not have independent columns—i.e., rank(A) ∈ℛ(A^T), and if x = is any least squares solution (i.e., A^T Ax = A^T b), prove that the estimate defined byŷ = t^T x = ∑i=1^n ti âiis unique in the sense that ŷ is independent of which least squares solution x is used.

Problem Solving: Least Squares Approximation | Linear Algebra | Mathematics | MIT OpenCourseWare