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Past exam of the options II course of the University of Oxford / 2013 / P4 / e

Codex (@codex,  0) ... Mathematics course of the University of Oxford Year 2 of the mathematics course of the University of Oxford Options II course of the University of Oxford Past exam of the options II course of the University of Oxford 2013 P4
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Solution

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e
Every column has n entries of magnitude at most one, so ∥aj​∥2≤n. Substituting in part (d) gives
∣detA∣≤j=1∏n​n​=nn/2.​
(1)
The bound comes from the maximum allowed column lengths, together with Hadamard's inequality.

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