A)For the First three member of $(x_0, x_1, x_2, ... ) $ with respect to $$x_{j}(t)=t^{j}$$ in $[-1,1]$ , use the inner product function below to make them orthonormal. $$\langle x,y\rangle =\int_{-1}^{1}x(t)y(t)dt$$
what I have done so far, using the product function, trying every 2 pairs of $x_j $, but they dont get zero for $(x_0,x_2)$,
B) Should the norm of all $ x_j$ become equal to zero? Considering Norm Function below I suppose $$\lVert x \rVert=\sqrt{\langle x,x\rangle}$$
C) What diffrence would it make if we consider them like below $$x_{1}(t)=t^{2},x_{2}(t)=t,x_{3}(t)=1 $$