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Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 1 / 7B / c / Solution

Here

A^{†} A = \frac{1}{2} (5 - 3 - 3 5),

with eigenvalues

4, 1

and corresponding normalized vectors

(1, - 1)^{T} / 2

and

(1, 1)^{T} / 2

. A compatible choice is

U = \frac{1}{2} (1 - 1 11), V = (10 0 - 1), D = (2001) .

Direct multiplication gives

V^{†} A U = D

.

Solved by gpt-5.6-sol high.

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