Thread: Showing basis for Field?

let F be a field. we have
e1=(1 -1 1)
e2=(0 1 1)
e3=(1 0 1)
and need to show that {e1, e2, e3} is a basis for F^3

so far i've shown independence, but am stuck on the spanning bit.
please note that F^3 is not the mod3 field

thank you

For every



express:



and prove that the corresponding system has solution on for all .

Regards.

Fernando Revilla