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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2021

Paper 2

Choose the least $k\geq1$ such that
$$
(f-\alpha I)^kv=0.
$$
Then
$$
w=(f-\alpha I)^{k-1}v
$$
is nonzero by minimality, and
$$
(f-\alpha I)w=0.
$$
\b[Therefore $fw=\alpha w$, so $w$ is the required nonzero <eigenvector>.]

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 2 / 8E / b / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 2 / 8E / b / i / Solution

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Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 2 / 8E / b / i / Solution

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