A First Course in Linear Algebra · Problem M12

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · vector-space-axioms

Problem

Let

V

be the set

\mathbb{C}^2

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

\begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix} z \\ w \end{bmatrix} = \begin{bmatrix} y + w \\ x + z \end{bmatrix}

Determine whether or not

V

is a vector space with these operations.