SOLUTION: Let f,g, element F(R,R) be the function defined by f(t)=e^rt and g(t)=e^st, where r cannot equal s. prove that f and g are linearly independent in F(R,R)
Algebra ->
College
-> Linear Algebra
-> SOLUTION: Let f,g, element F(R,R) be the function defined by f(t)=e^rt and g(t)=e^st, where r cannot equal s. prove that f and g are linearly independent in F(R,R)
Log On
Question 346626: Let f,g, element F(R,R) be the function defined by f(t)=e^rt and g(t)=e^st, where r cannot equal s. prove that f and g are linearly independent in F(R,R) Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
By the zero product property, or
The first case can never happen since for all values of
The second case can only happen when
When .
Since this is not the case, then f and g are linear independent. only when
