 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/7/solution

(1, 1)

and

(1, - 1)

are eigenvectors, with respective eigenvalues

cosh ϕ + sinh ϕ

and

cosh ϕ - sinh ϕ

. The exponential definitions reduce these to

λ_{+} = e^{ϕ}, λ_{-} = e^{- ϕ} .

ϕ = 0

they coincide and the matrix is the identity.

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