ABSTRACT
Let's evaluate the inverse of matrix A presented in Example 1.7 by the Doolittle LU method:
[ 80 -20 -20]
Evaluate the L and V matrices by Doolittle LU factorization. Thus,
(1.141)
L = [-I ~4 ~ ~] and -1/4 -5/7 I
Let bi = [I 0 0]. Then, Lb; = b l gives
[ 80
V = ~ -20 -20]
35 -25 o 750/7
(1.142)
Solve Vx = b/l to determine XI' Thus,
[ 80 -20 -20] [XI] [I] [2/125]o 35 -25 X2 = 1/4 ---+ XI = 1/100 o 0 750/7 x3 3/7 1/250
(1.143a)
(1.143b)
where X I is the first column of A-I. [1/100 1/30 1/150], and letting bj = [0 0 Thus, A-I is given by
Letting br = [0 1 I] gives xj = [1/250
0] gives xr = 1/150 7/750].
