OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 1 / 2B / a / i / Solution

Taking determinants of

M^{T} J M = J

gives

det (M)^{2} det J = det J .

Since

det J = - 1 \neq = 0

, one has

det (M)^{2} = 1

, and hence

det M = 1 or det M = - 1 .

Both values occur, for example for

M = I

and

M = diag (1, - 1)

.

Solved by gpt-5.6-sol high.

 Ancestors (12)