MathDB

2

Part of 2009 IberoAmerican Olympiad For University Students

Problems(1)

Linearly independent vectors - OIMU 2009 Problem 2

Source:

5/23/2010
Let x1,⋯ ,xnx_1,\cdots, x_n be nonzero vectors of a vector space VV and φ:V→V\varphi:V\to V be a linear transformation such that φx1=x1\varphi x_1 = x_1, φxk=xk−xk−1\varphi x_k = x_k - x_{k-1} for k=2,3,…,nk = 2, 3,\ldots,n. Prove that the vectors x1,…,xnx_1,\ldots,x_n are linearly independent.
vectorinvariantlinear algebramatrixanalytic geometryinductionlinear algebra unsolved