Question

examine the following sets for linear independence:u1= e^x ,u2= e ^−x

Answer 1

\[u _{1}=e^{x}, u _{2}=e^{-x}, \]

Answer 2

PLZ HELP

Answer 3

you know the definition of linear independence?

Answer 4

u1=e^x, u2=e^-x, are independent if there exist two scalar a,b such that:
a(e^x)+b(e^-x)=0

Answer 5

i know c1u1+c2u2=0; if c1 and c2 is zero then its called linear independence

Answer 6

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.

Answer 7

great