Wronskian of $$$t$$$, $$$3 t - 1$$$
Your Input
Calculate the Wronskian of $$$\left\{f_{1} = t, f_{2} = 3 t - 1\right\}$$$.
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, $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & 3 t - 1\\\left(t\right)^{\prime } & \left(3 t - 1\right)^{\prime }\end{array}\right|.$$$
Find the derivatives (for steps, see derivative calculator): $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right|$$$.
Find the determinant (for steps, see determinant calculator): $$$\left|\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right| = 1$$$.
Answer
The Wronskian equals $$$1$$$A.