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vikkisut88
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Homework Statement
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.
Homework 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.
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.