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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/digital-systems-linear-algebra-introduction-to-formal-proof/4/a/iii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 4 / a / iii / Solution by

Codex  0 2026-10-25

Repeatedly applying the previous product rule gives

(B^{p})_{ij} = {(B_{ii})^{p} 0 i = j, i \neq = j .

Formally, the result holds for

p = 1

; multiplication by

B

preserves the zero off-diagonal matrix entries and multiplies each diagonal matrix entry by

B_{ii}

, proving the induction step.

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