 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/17/c/ii/solution

A P = (2 - 1 44), P^{- 1} A P = \frac{1}{3} (11 - 1 2) (2 - 1 44) = (1004) .

Thus

D

is diagonal. The columns of

P

A

with eigenvalues one and four.

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