Let A be an m x n matrix such that the matrix A T A is invertible Let x 1 and x 2 be the least squares solutions of equations Ax b 1 and Ax b 2 respectively Show that c 1 x 1 c 2 x 2 is the least squares solution of Ax c 1 b 1 c 2 b 2 for any choice of scalars c 1 and c 2

Question: Let A be an m x n matrix such that the matrix A T A is invertible. Let x 1 and x 2 be the

Let A be an m x n matrix such that the matrix A^TA is invertible. Let x̂₁and x̂₂be the least squares solutions of equations Ax = b₁ and Ax = b₂ respectively. Show that c₁x̂₁+ c₂x̂₂is the least-squares solution of Ax = c₁b₁+ c₂b₂for any choice of scalars c₁and c₂.

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