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Matrix Differentiated (Posted on 2019-05-24) Difficulty: 3 of 5
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).

No Solution Yet Submitted by Danish Ahmed Khan    
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Remark on: clarifcation | Comment 2 of 3 |
(In reply to clarifcation by Daniel)

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
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