Chapter 4 - Vector Spaces - 4.5 Linear Dependence and Linear Independence - True-False Review - Page 296: i

False

We have the remarks from Theorem 4.5.23, If $W[ f_1, f_2,..., f_k ](x) = 0$ for all $x$ in $I$, Theorem 4.5.23 gives no information as to the linear dependence or independence of $\{ f_1, f_2,..., f_k \}$ on $I$. Even if the Wronskian of a set of functions is identically zero at every point of an interval $I$, we still can not conclude anything about the set of functions.