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Linear map

Source: Iranian National Olympiad (3rd Round) 2006

September 21, 2006
linear algebralinear algebra unsolved

Problem Statement

f:Rn⟶Rmf: \mathbb R^{n}\longrightarrow\mathbb R^{m} is a non-zero linear map. Prove that there is a base {v1,…,vnm}\{v_{1},\dots,v_{n}m\} for Rn\mathbb R^{n} that the set {f(v1),…,f(vn)}\{f(v_{1}),\dots,f(v_{n})\} is linearly independent, after ommitting Repetitive elements.
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