4.4 Linear equation solution and matrix factorization 4.4.1 Gaussian Method (1)Forward Elimination (2)Back Substitution b) a a唱 a d d (0) 02n X2 0 咄 () 02n X2 b : : : : : d (0) 0 a唱 a a 1) nn 1 a a 1 ) () 12 3 0 1 a X2 0 1 a 2) 0 0 a X3 0 0 1 : a 古 b . a a Xn 0 0 Xn4.4.1 Gaussian Method (1) Forward Elimination (2) Back Substitution                (1) (1) 2 (1) 1 2 1 (1) (1) 3 (1) 2 (1) 2 (1) 23 (1) 22 (1) 1 (1) 13 (1) 12 0 0 1 n n nn n n n n b b b x x x a a a a a a a a a                      (0) (0) 2 (0) 1 2 1 (0) (0) 3 (0) 2 (0) 1 (0) 2 (0) 23 (0) 22 (0) 21 (0) 1 (0) 13 (0) 12 (0) 11 n n n nn n n n n b b b x x x a a a a a a a a a a a a                           (2) (2) 3 (2) 2 (2) 1 3 2 1 (2) (2) 3 (2) 3 (2) 33 (2) 2 (2) 23 (1) 1 (1) 13 (1) 12 0 0 0 0 0 1 1 n nn n n n n n b b b b x x x x a a a a a a a a a                          ( ) (3) 3 (2) 2 (2) 1 3 2 1 (3) 3 (2) 2 (2) 23 (1) 1 (1) 13 (1) 12 0 0 0 1 0 0 1 0 1 1 n n n n n n b b b b x x x x a a a a a a      