Linear Algebra Done Right · Problem 3E.17

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · quotient-spaces

Problem

Suppose UU is a subspace of VV such that dim⁡V/U=1\dim V/U = 1. Prove that there exists φ∈L(V,F)\varphi \in \mathcal{L}(V, \mathbf{F}) such that null⁡φ=U\operatorname{null} \varphi = U.

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