anonymous
  • anonymous
examine the following sets for linear independence:u1= e^x ,u2= e ^−x
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[u _{1}=e^{x}, u _{2}=e^{-x}, \]
anonymous
  • anonymous
PLZ HELP
anonymous
  • anonymous
you know the definition of linear independence?

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anonymous
  • anonymous
u1=e^x, u2=e^-x, are independent if there exist two scalar a,b such that: a(e^x)+b(e^-x)=0
anonymous
  • anonymous
i know c1u1+c2u2=0; if c1 and c2 is zero then its called linear independence
anonymous
  • anonymous
multiply both sides by e^x to get: a(e^2x)+b=0 --> a(e^2x)=-b , which only has the solution (a,b)=(0,0).. (a,b)=(0,0) satisfies the definition since 0(e^x)+0(e^-x)=0, and hence they are linearly independent.
anonymous
  • anonymous
great

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