Linear Eqns of Higher Order: f(x)=2cos(x)+3sin(x), g(x)=

[bearej50]

f(x) = 2cos(x) + 3sin(x), g(x) = 3cos(x) - 2sin(x)

Determine whether the pair of functions is linearly independent or linearly dependent on the real line.

 

[DrMike]

f(x) = 2cos(x) + 3sin(x), g(x) = 3cos(x) - 2sin(x)

Determine whether the pair of functions is linearly independent or linearly dependent on the real line.

Solve af(x)+bg(x)=0 for a and b.

If you get a unique solution a=b=0, then f and g are linearly independent. That's the definition of linearly independent : \(\displaystyle v_1,v_2,...,v_n\) are linearly independent if and only if the system \(\displaystyle a_1v_1+a_2v_2+...+a_nv_n=0\) has only one solution \(\displaystyle a_1=a_2=...=a_n=0\).