A First Course in Linear Algebra · Problem T21

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · vector-space-cancellation

Problem

Suppose that

V

is a vector space, and

\mathbf{u}, \mathbf{v}, \mathbf{w} \in V

. If

\mathbf{w} + \mathbf{u} = \mathbf{w} + \mathbf{v}

, then

\mathbf{u} = \mathbf{v}