Write a matlab script 'lin_solve' to solve linear systems of algebraic equations (Ax = b) of any size N, using LU factorization method. The script should call 'lu_factor' to perform the factorization in to U, an upper triangular matrix and L, a lower unit triangular matrix. The script should then call two functions 'forward_solve' and 'back_solve' to solve the resulting systems of equations. 1. (4 points) Decompose the following matrices in to a lower unit triangular matrix and an upper triangular matrix: [424] (a) A = 259 (b) (C) (d) [469] [1 1 1] A = 2 3 5 4 6 8] [132] A = 285 1 11 4 1 -2 -2 -3 3 -9 0 -9 -1 2 4 7 -3 -6 26 2 2. (2 points) Modify the 'lu_factor script to solve the following system of equations using Gauss elimination without pivoting. 8 0 -6 A=0 -8 -2 4 6 4 0 A = A = 7 3. (2 points) Solve the following system of equations using LU factorization. 2 1 -1 2] [5] 4 5 -36 -2 4 5-2 6 11 -4 8 b = a + N