Let A and B be two n×n matrices with real entries.
Define the function f : R → R by
f(x) = det(A + Bx)
(i) Show that f(3)(x) = 3! det B.
(ii) Show that in general f(n)(x) = n! det B.
f(n)(x) is the nth derivative of f(x).
(In reply to clarifcation
This occurred to me as well.
Perhaps DAK intended to state in (i) that n=3. So then the second part of the problem is a generalisation of part (i)?
Posted by FrankM
on 2019-05-27 13:13:28