A First Course in Linear Algebra · Problem M11

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · vector-space-axioms

Problem

Let

V

be the set

\mathbb{C}^2

with the usual vector addition, but with scalar multiplication defined by

\alpha \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} \alpha y \\ \alpha x \end{bmatrix}

Determine whether or not

V

is a vector space with these operations.