Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 1 / 7B / d / Solution

Apply the matrix determinant lemma to $HP-\lambda I=(H-\lambda I)-Hu,u^T$: its determinant is ${\chi }_H(\lambda )[1-u^T(H-\lambda I{)}^{-1}Hu]$.

Solved by gpt-5.6-sol high.