Let K ⊆ L {\displaystyle {}K\subseteq L} be a finite field extension, and let v 1 , … , v n ∈ L {\displaystyle {}v_{1},\ldots ,v_{n}\in L} denote elements that form a K {\displaystyle {}K} -basis of L {\displaystyle {}L} . Let x ∈ L {\displaystyle {}x\in L} , x ≠ 0 {\displaystyle {}x\neq 0} . Show that also x v 1 , … , x v n ∈ L {\displaystyle {}xv_{1},\ldots ,xv_{n}\in L} form a K {\displaystyle {}K} -basis of L {\displaystyle {}L} .
be a
finite
field extension, and let
denote elements that form a
-basis
of 
. Let
, 
.
Show that also
form a -basis of .
