 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2/17/b/iii/solution

Let

D_{β} = diag (β_{1}, \dots, β_{n})

and

D_{γ} = diag (γ_{1}, \dots, γ_{n})

. The specified entries mean

C = D_{β} A D_{γ}

∣ C ∣ = (i = 1 \prod n β_{i}) (j = 1 \prod n γ_{j}) ∣ A ∣ .

This is also the direct row- and column-scaling rule, and it includes zero scaling factors.

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