Please provide proof for this theorem...

by Juan Tamad   Last Updated November 13, 2017 10:20 AM

Lemma 1. Let A=(aij)∈C^m×n, and let ε>0 . Then for each k∈{0,1,2,⋯,mn} k∈{0,1,2,⋯,mn} the number of all possible (ε,k)-perturbations of A is the same as the number of ways of selecting k objects from “mn” distinct objects without regard to the order.

Theorem 1. Let A=(aij)∈Cm×n,x∈CA=(aij)∈Cm×n,x∈C and ε>0 . Then for each k∈{0,1,2,⋯,mn}k∈{0,1,2,⋯,mn} , the number of all possible (ε,k) -perturbation of A is the binomial coefficient of the term x^k in the binomial expansion of (1+x)^mn. By changing the positive integer p:=mn over the set of positive integers N, we generate the Pascal’s triangle.

Tnx, a lot guys... anyway this is about my report in linear algebra... according to the author(and I emailed him already) the proof of this two are straighforward ^^, it does not appear to me... Please help guys... thank U...



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