Problem 4. (a) Write your own LU factorization code (i.e. a code that converts a given matrix into its lower triangular and upper triangular multiplicative components) and (b) LU solution code (i.e. a code that solves a linear system given the LU decomposition of the matrix and the right-hand side vector). (c) Use your codes to factor and solve the following linear systems: 2.1756 4.0231 2.1732 5.19671rxi 8 -4.0231 6.0000 0.0000 1.1973 |)X2(- [A]{x} = {b} = 1 6 -6.1593 -1.0000-5.2107 1.1111 0.0000X3 6.0235 7.0000 0.0000-4.1561 2.121-3.460 0.000 5.217 1 0.000 5.193 2.197 4.206 y2 5.132 1.414 3.141 0.0001) -3.111-1.732 2.718 5.212](y4 By -2.101 6.824 Report both the matrix decomposition and the solution vector for each system. The two codes should be submitted along with a written description of their operation (this description does not need to be as detailed as a pseudocode)