題組內容

7. (20%) Given $\varphi_1(t) = 1$, $\varphi_2(t) = t$, $\varphi_3(t) = 3t^2 - 1$,

(ii) Are \( \varphi_1(t) \) and \( \varphi_3(t) \) mutually orthogonal over the interval (-1, 1)? Why or why not?