Wronskin determinantti funktioille $$$t$$$, $$$t^{2}$$$

Laske Wronskin determinantti funktioille $$$\left\{f_{1} = t, f_{2} = t^{2}\right\}$$$.

Wronskin determinantti määritellään seuraavalla determinantilla: $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}f_{1}\left(t\right) & f_{2}\left(t\right)\\f_{1}^{\prime}\left(t\right) & f_{2}^{\prime}\left(t\right)\end{array}\right|.$$$

Meidän tapauksessamme pätee $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & t^{2}\\\left(t\right)^{\prime } & \left(t^{2}\right)^{\prime }\end{array}\right|.$$$

Laske derivaatat (vaiheet: katso derivointilaskuri): $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & t^{2}\\1 & 2 t\end{array}\right|$$$.

Laske determinantti (vaiheet: ks. determinanttilaskin): $$$\left|\begin{array}{cc}t & t^{2}\\1 & 2 t\end{array}\right| = t^{2}$$$

Wronskin determinantti on $$$t^{2}$$$A.