A First Course in Linear Algebra · Problem M14

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · vector-space-axioms

Problem

Let

V

be the set

M_{22}

with the usual addition, but with scalar multiplication defined by

\alpha A = \mathcal{O}_{2,2}

for all

2 \times 2

matrices

A

and scalars

\alpha

. Determine whether or not

V

is a vector space with these operations.