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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 8A / d / Solution

(1, 0, 1)^{T}, (0, 1, 0)^{T}, (1, 0, - 1)^{T}

are eigenvectors of

B

with eigenvalues

2, 1, 0

. Applying the exponential to these eigenspaces gives

e^{B} = (1 + e^{2}) /2 0 (e^{2} - 1) /2 0 e 0 (e^{2} - 1) /2 0 (1 + e^{2}) /2 .

Solved by gpt-5.6-sol high.

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