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Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 5B / b / Solution

If

A

has full column rank, then for every nonzero

h

,

h^{T} A^{T} A h = ∥ A h ∥^{2} > 0.

Thus

A^{T} A

is positive definite and invertible, and the normal equation has the unique solution

c^{*} = (A^{T} A)^{- 1} A^{T} y .

Solved by gpt-5.6-sol high.

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