2 2 0] [Xl]

Performing back substitution yields xi = [0.60 1.00 0.40]. Repeating the process for bI = [20 10 20] yields

[ I 0 O][b;] [20]b;=20

-I 14 lOb; = lOb; = 15 -1/4 -5/7 I b; 20 b; = 250/7

-~~ =~~] [;~] = [ 7~ ];~: ~~~ o 750/7 X3 250/7 x3 = 1/3

(1.138)

When pivoting is used with LV factorization, it is necessary to keep track of the row order, for example, by an order vector o. When the rows of A are interchanged during the elimination process, the corresponding elements of the order vector 0 are interchanged. When a new b vector is considered, it is processed in the order corresponding to the elements of the order vector o.