Wronskian of $$$t$$$, $$$t^{2}$$$
Your Input
Calculate the Wronskian of $$$\left\{f_{1} = t, f_{2} = t^{2}\right\}$$$.
Solution
The Wronskian is given by the following determinant: $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}f_{1}\left(t\right) & f_{2}\left(t\right)\\f_{1}^{\prime}\left(t\right) & f_{2}^{\prime}\left(t\right)\end{array}\right|.$$$
In our case, $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & t^{2}\\\left(t\right)^{\prime } & \left(t^{2}\right)^{\prime }\end{array}\right|.$$$
Find the derivatives (for steps, see derivative calculator): $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & t^{2}\\1 & 2 t\end{array}\right|$$$.
Find the determinant (for steps, see determinant calculator): $$$\left|\begin{array}{cc}t & t^{2}\\1 & 2 t\end{array}\right| = t^{2}$$$.
Answer
The Wronskian equals $$$t^{2}$$$A.