Chapter 8.1, Problem 2TFR

True-False Review

For Questions (a)-(j), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem in fact from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

If $y_1,y_2,\cdots ,y_n$ are solutions to a regular $n\text{th}$-order linear homogenous differential equation such that $W\left[y_1,y_2,\cdots ,y_n\right]\left(x\right)$ is zero at some points of $I$ and nonzero at other points of $I$, then $\left\{y_1,y_2,\cdots ,y_n\right\}$ is a linearly independent set of functions.