 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof-resit/6/b/i/solution

A^{T} A x = A^{T} b .

R

Q^{T} Q = I

. Hence, for every nonzero

u

u^{T} A^{T} A u = ∥ A u ∥_{2}^{2} > 0

. Thus

A^{T} A

is a symmetric positive-definite matrix and the displayed square system is nonsingular.

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