(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V = {differentiable f:R -> R}, a vector space over R. Take g1,g2,g3 in V where g1(x) = e[tex]^{}x[/tex], g2(x) = e[tex]^{}2x[/tex] and g3(x) = e[tex]^{}3x[/tex].

Show that g1, g2 and g3 are distinct.

2. Relevant equations

If g1-g3 are linearly independent, it means that for any constant, k in F (field) then they all = 0 when g1k1 + g2k2 + g3k3 = 0.

3. The attempt at a solution

I have the idea to choose a value of x in R so that g1(x), g2(x), g3(x) are distinct, but I'm not exactly sure where to go from there because apart from choosing x=0 then for the rest of the time then they must be distinct as they all have different values. I'm just not sure how I prove this.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proving that g1,g2,g3 are linearly independent

**Physics Forums | Science Articles, Homework Help, Discussion**