Symmetric 2x2-matrices/Vector space/Exercise

Show that the set of all "symmetric“ ${}2\times 2$-matrices over a field ${}K$, that is, matrices of the form

${\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}}$

satisfying the condition

${}a_{12}=a_{21}\,,$

is, with componentwise addition and componentwise scalar multiplication, a ${}K$-vector space.

Create a solution