Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 1F / b

Table of contents
- Solution b

Solution

Move the first

n - k

columns of

A = (0 N M 0)

past its last

k

columns. This requires

k (n - k)

column interchanges and produces the block diagonal matrix

(M 0 0 N) .

Each interchange reverses the determinant's sign, so part (a) gives

det A = (- 1)^{k (n - k)} (det M) (det N) .

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