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 $\R$.