The system 2x = -6, -4x + 3y = 3, x + 4y-z = 7, is in lower triangular form.
(a) Formulate a method of Forward Substitution to solve it.
(b) What happens if you reduce the system to the (upper) triangular form using the algorithm in this section?
(c) Devise an algorithm that uses our linear system operation to reduce a system to lower triangular form and then solve it by Forward Substitution.
(d) Check your algorithm by applying it to one or two of the systems in Exercise 1.1.1. Are you able to solve them in all cases?