Chapter 6.1, Problem 29E

To determine

(a)

To show:

If set of functions $f_1,\mathrm{...},f_m$ are linearly independent on $\left(-1,1\right)$, then they are linearly independent on $\left(-\infty ,\infty \right)$

To determine

(b)

To show:

An example in which set of functions $f_1,...,f_m$ are linearly independent on $\left(-\infty ,\infty \right)$ but not necessarily in the interval $\left(-1,1\right)$.