1. ## Wronskian computation

Given set of functions: 1, x, x^2, x in any interval; compute the Wronskian of this given set of functions and then determine whether the function is linearly dependent or independent. Could someone explain how to go about this? Thanks,

Jim

2. Hi

For three functions $f_1,\,f_2,\,f_3$, the wronskian is $W(x)=\left| \begin{array}{ccc}
f_1(x) & f_2(x) & f_3(x)\\
f_1'(x) & f_2'(x) & f_3'(x)\\
f_1''(x) & f_2''(x) & f_3''(x)
\end{array}
\right|$
and the functions are linearly independent if the wronskian is nonzero.