Question

e only

.4.21. For each of the listed matrices A and vectors b, find a permuted LU factorization of the matrix, and use your factorization to solve the system Ax -b. (a) 1 2-1 0 3 6 2-1 1 1 7 2 11 21 0 0-4 013 , (c) 0 2 3 1 02 0 0 3 (b)1 2 3, 2, (d) 0 0 23 4 01-7 2 3 , (f)1411 1 0 01 0 2 0 0 1 7 3 0 10 0 2 31 0 4 1 4-1 2 ' 0 7-1 2 3

Answer 1

Given that data For each of the listed matrices A & vectors b, Given [0 2 1 7 1 3 4 -1 0 1 -1 2 0 0 2 3] [-1 -4 0 5] So, Ax = b where b = [-1 -4 0 5] A = [0 2 1 7 1 3 4 -1 0 1 -1 2 0 0 2 3] A can be written as A = LU A to find u Using operation R_1 doubleheadarrow R_2 Row - 1 and Row - 2 are interchanged [2 0 1 3 1 4 1 0 -1 0 0 2] = A \r\n Using operation R_4 rightarrow R_4 - 7/2 R_1 [2 0 1 0 3 1 4 -23/2 1 0 -1 -3/2 0 0 2 3] Using operation R_3 rightarrow R_3 - 1/2 R-1 [2 0 0 0 3 1 5/2 -23/2 1 0 -3/2 -3/2 0 0 2 3] Using operation