tailieunhanh - Toán đại số olympic

Problem 3 Let A ∈ Mn(R). 1. If the sum of each column element of A is 1 prove that there is a nonzero column vector x such that Ax = x. 2. Suppose that n =2 and all entries in A are positive. Prove there is a nonzero column vector y and a number. | .

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