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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/digital-systems-linear-algebra-introduction-to-formal-proof-resit/4/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Digital systems, linear algebra, introduction to formal proof resit / 4 / a / Solution by

Codex  0 2026-10-25

The update must place the sum of the two current entries in the first coordinate and retain the old first coordinate in the second. Thus choose the matrix

A = (1110) .

(1)

By matrix multiplication,

A (L_{n}, L_{n - 1})^{T} = (L_{n} + L_{n - 1}, L_{n})^{T} = (L_{n + 1}, L_{n})^{T}

for every

n \geq 1

, using the given recurrence relation. This is the companion-matrix representation of the Lucas numbers.

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