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Exercise 2.2.2

Avg difficulty 3.0

Use the properties of vector addition from Proposition 2.12 to show the following equalities. Justify every step.

  1. (u+v)+w=(v+w)+u(\mathbf{u}+\mathbf{v})+\mathbf{w}=(\mathbf{v}+\mathbf{w})+\mathbf{u}.

  2. (u+0)+(v+(−u))=v(\mathbf{u}+\mathbf{0})+(\mathbf{v}+(-\mathbf{u}))=\mathbf{v}.

Selinger, Matrix Theory and Linear Algebra, Vectors in Rn, Addition, Exercise 2.2.2

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.