 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ia/paper-1/7b/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

det (A - λ B) = - (λ - 2) (λ - 4) (3 λ - 10) .

The generalized Rayleigh quotient is maximized by the largest generalized eigenvalue,

4

. Solving

(A - 4 B) v = 0

gives

v \neq = 0 max F (v) = 4, v \propto (- 1, 2, 0)^{T} .

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