A First Course in Linear Algebra · Problem T23

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · vector-space-cancellation

Problem

Suppose

V

is a vector space,

\mathbf{u} \neq \mathbf{0}

is a vector in

V

and

\alpha, \beta \in \mathbb{C}

. If

\alpha \mathbf{u} = \beta \mathbf{u}

, then

\alpha = \beta