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matrix product is nonzero

Source: VJIMC 2011 2.1

June 1, 2021
linear algebramatrix

Problem Statement

Let n>kn>k and let A1,…,AkA_1,\ldots,A_k be real n×nn\times n matrices of rank n−1n-1. Prove that A1⋯Ak≠0.A_1\cdots A_k\ne0.
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