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).


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