Functions, Interval. See attached file for full problem description.
Given the set of functions
f1(t) = A1*exp(-t)
f2(t) = A2*e^(-2t)
Defined on the interval (0, infinity).
(a) Find A1 such that f1(t) is normalized to unity on (0, infinity). Call this function PHI_1(t).
(b) Find B such that PHI(t) and f2(t) - B*PHI(t) are orthogonal on (0, infinity). Normalize this new function and call it PHI_2(t).
(c) Do this for the third function, e^(-3t). That is, chooses C and D such that f3(t) - C*PHI_2(t) - D*PHI_1(t) is orthogonal to both PHI_1(t) and PHI_2(t). Normalize it and call it PHI_3(t). Comment on the feasibility of continuing this procedure.
The solution shows hot to normalize the functions and find the orthogonal function in detail.