Let A be a matrix of the order n x n and for i = 1, , m be b⁽ⁱ⁾ matrixes of order n 1.

(a) Write an algorithm to simultaneously solve a linear equation system, Ax⁽ⁱ⁾ = b⁽ⁱ⁾, using factorization P A = LU with partial pivot method.

(b) Give a program/code (LU-Factorization-extended.m), in Octave or Matlab, to solve the linear equation system Ax⁽ⁱ⁾ = b⁽ⁱ⁾, using factorization P A = LU with partial pivot method.

(c) Consider A as a n n with

[A]_ij = { i + j, i j

i j, i > j}

Using the code proposed for LU-Factorization-extended.m, find if possible, A1 to n = 5 and n = 15.