Show that $\langle \cdot , \cdot \rangle$ is an inner product on $\mathbb { R } _ { n - 1 } [ X ]$, where $$\langle P , Q \rangle = \sum _ { k = 1 } ^ { n } P \left( a _ { k } \right) Q \left( a _ { k } \right).$$
Show that $\langle \cdot , \cdot \rangle$ is an inner product on $\mathbb { R } _ { n - 1 } [ X ]$, where
$$\langle P , Q \rangle = \sum _ { k = 1 } ^ { n } P \left( a _ { k } \right) Q \left( a _ { k } \right).$$