(a) Write a program for solving linear systems by Cholesky’s method and apply it to Example 2 in the text, to Probs. 7–9, and to systems of your choice. (b) Apply the factorization part of the program to the following matrices (as they occur in (9), (with c_j = 1), in connection with splines).

Data from Prob. 7

Show the factorization and solve.

  9x₁ +    6x₂ + 12x₃ = 17.4  6x₁ + 13x₂ + 11x₃ = 23.612x₁ + 11x₂ + 26x₃ = 30.8