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

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- May 12th 2008, 02:35 PMJim NewtWronskian 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 - May 13th 2008, 11:58 AMflyingsquirrel
Hi

For three functions $\displaystyle f_1,\,f_2,\,f_3$, the wronskian is $\displaystyle 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.