$2 Matrix Factorization-Matrix Form of GE 记为 k+1,k k air Factorize A first, then for every you only have to ix*/ 记U solve two simple triangular systems Ly=b and Ux=y m A的’U /*LU factor- n§2 Matrix Factorization – Matrix Form of G.E. = −1 Lk 1 . . . 1 1 , 1, n k k k m m + = − − − − 1 1 1 2 1 1 ... L L Ln 1 1 1 mi, j 记为 L 单位下三角阵 /* unitary lower-triangular matrix */ 记 U = ( ) (2) 2 (2) 22 (1) 1 (1) 12 (1) 11 . . . ... ... ... n nn n n a a a a a a  A = LU A 的 LU 分解 /* LU factorization */ Hey hasn’t GE given me enough headache? Why do I have to know its matrix form??! When you have to solve the system for different with a fixed A. b  Could you be more specific, please? Factorize A first, then for every you only have to solve two simple triangular systems and . b  Ly b   = Ux y   =