Wait, is the set as you wrote, or ?
The set is:
{1, cos(2x) 3*(sin(x))^2}
I figure that:
C1(1 +C2(cos(2x) + C3*(3*sin(x))^2 =0
That gives us:
C1(1) + C2(Cos(0) + C3(3(sin(0))^2 = 0
Thus C1 + C2 + 0 = 0
So:
C1 + C2 = 0
How do I find C3?
If my process is correct...Linear dependence exists if either C1 , C2 or C3 are non zero...
Hence one of the terms changes...
1, cos 2x, 1-cos3x thus our eq'n should look like:
c1(1) + c2(cos 2x) +c3(1-cos3x) = 0
That gives us
c1+c2=0 while c3=1?
Thus the solution is that
matrix looks like |1|
|0|
|0|
Thus the solution is dependent because one of the values is non-zero...
Don't think of the sine as functions, think of them as unknowns - call them , and : . So, we want to find integers such that , by the definition of linear dependence.
Substitute in the into TPH's equality and stick everything on one side. You should have something of the form and thus your set is not linearly independent.