Mathematics · Numerical Analysis

Consider the linear system Ax = b, where A = [aij], i, j = 1, 2, 3 and aii ≠ 0 for i = 1, 2, 3 is a real matrix. Let D = diag(a11, a22, a33). Given that: D-1A = ⌈ 1 1 -2 ⌉ ⌊ 3 1 2 ⌋ ⌊ 1 1 1 ⌋, D-1b = ⌈ 4 ⌉ ⌊ 4 ⌋ ⌊ 1 ⌋ Consider the following two statements: S1: The approximation of x after one iteration of the Jacobi scheme with initial vector x(0) = [1 1 1]T is x(1) = [5 -1 -1]T. S2: There exists an initial vector x(0) for which the Jacobi iterative scheme diverges. Which of the following is correct?