## Exponential Functions are Linearly Independent

## Problem 73

Let $c_1, c_2,\dots, c_n$ be mutually distinct real numbers.

Show that exponential functions

\[e^{c_1x}, e^{c_2x}, \dots, e^{c_nx}\]
are linearly independent over $\R$.

Let $c_1, c_2,\dots, c_n$ be mutually distinct real numbers.

Show that exponential functions

\[e^{c_1x}, e^{c_2x}, \dots, e^{c_nx}\]
are linearly independent over $\R$.