
To explain: the difference between Gaussian and Gauss-Jordan elimination and advantage of Gauss-Jordan elimination

Answer to Problem 10RCC
Gauss-Jordan elimination transforms the augmented matrix into reduced row- echelon form
Gaussian elimination only provides the row-echelon form.
Advantage:
Gauss-Jordan elimination does not require the use of back-substitution to obtain the solution
Explanation of Solution
Gauss-Jordan elimination differs from Gaussian elimination in that Gauss-Jordan elimination transforms the augmented matrix of a linear system into reduced row- echelon form while Gaussian elimination only provides the row-echelon form.
The advantage of this procedure is that Gauss-Jordan elimination does not require the use of back-substitution to obtain the solution for the linear system.
This is because all the leading entries of an augmented matrix in reduced row-echelon form contain only leading 1s and contain zeros for all the other entries.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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