Let the functions $a_{ij}(t)$ , $1\leq i$ , $j\leq 2$ , are continuous on $|t-a|\leq T$ . Let $f(t)$ be fundamental matrix defined by $2$ solutions $x^1(t)$ , $x^2(t)$ of a homogeneous system $dx/dt = A(t)x$ , with $A(t)=(a_{ij}(t))$
Show that the Wronskian $W(t)$ , defined to be $\det f(t)$ , satisfies the differential equation $$ dW(t)/dt = \left(\sum_{i=1}^2 a_{ii}(t) \right) W(t) $$