Sample Matrix Independence Test/Examples

Examples of Sample Matrix Independence Test

Example: Linearly Independent Solutions of $y - y = 0$

Prove independence of the solutions $e^x$, $e^{-x}$ to:

$y - y = 0$

Example: Linear Independence of Powers $1, x, \ldots, x^{n - 1}$

Let $V$ be the vector space of all continuous functions on $\R$.

Let $n \ge 1$ be an integer and define:

$S = \set {1, x, \ldots, x^{n - 1} }$

$S$ is a linearly independent subset of $V$.