Consider the following Gaussian-elimination/GaussJordan hybrid method for solving the

Chapter 6, Problem 6.1.16

(choose chapter or problem)

Consider the following Gaussian-elimination/GaussJordan hybrid method for solving the system (6.4). First, apply the Gaussian-elimination technique to reduce the system to triangular form. Then use the nth equation to eliminate the coefficients of xn in each of the first n 1 rows. After this is completed use the (n 1)st equation to eliminate the coefficients of xn1 in the first n 2 rows, and so on. The system will eventually appear as the reduced system in Exercise 12. a. Show that this method requires n3 3 + 3 2 n2 5 6 n multiplications/divisions and n3 3 + n2 2 5 6 n additions/subtractions. b. Make a table comparing the required operations for the Gaussian elimination, GaussJordan, and hybrid methods, for n = 3, 10, 50, 100.