Determine the number of operations needed to solve the system of equations of Exercise by...

Determine the number of operations needed to solve the system of equations of Exercise by using

(a) Gauss-Jordan elimination

(b) Gaussian elimination

Explain, by investigating in “all steps” mode, how the arithmetic operations are counted. Where exactly does Gaussian elimination gain over Gauss-Jordan elimination?

Exercise

There are many ways of solving systems of equations. In this exercise we introduce the method of Gaussian elimination.

The functions Gjalg and Galg have been written to give the reader practice at mastering the Gauss-Jordan and Gaussian algorithms by looking at patterns. Use the help facility to get information about these functions. Use these functions to see the difference in the algorithms in solving a system of three equations in three variables.

Solve the following system of equations using the function Gelim that performs Gaussian elimination with the “all steps” option. You get the same REF as you would with Gjelim, with a matrix called the echelon form of appearing along the way. Describe the characteristics of a matrix in echelon form. Describe the algorithm used in Gaussian elimination.