OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 2 / 7C / a / Solution

The characteristic polynomial is

det (A - λ I) = λ (λ - 1) .

For

λ_{1} = 0

and

λ_{2} = 1

, corresponding eigenvectors are

u_{1} = (21), u_{2} = (31) .

They are linearly independent, so the general homogeneous solution is

z (t) = α (21) + β e^{t} (31) .

Solved by gpt-5.6-sol high.

 Ancestors (11)