How would you show that the vectors (1,1,0) (1,0,1) and (0,1,1) generate F^3?
Do you simply put them in the matrix and solve the matrix or?
Since F^3 (whatever that is) has dimension three it means if you can show {(1,1,0),(1,0,1),(0,1,1)} are linearly independent it would mean they must spam the space.
Now say .
This means,