Problem 3 [4 pts]: Develop a computer program that solves matrix equation AX = B, using LU decomposition. Here A is an n x n square matrix, B is an n x m matrix. (Therefore the dimensions of the unknown matrix X is n x m.) You can use any existing function (e.g., lu(...) in MATLAB) to perform the LU decomposition on A, which will give you a permutation matrix? P, a lower triangular matrix L, and an upper triangular matrix U, such that PA = LU. But you should write your own program to solve LUX = PB, (equivalent to AX = B) taking advantage of the fact that L and U are triangular matrices. Your code should not use any built-in functions for solving linear systems or inverting a matrix. Demonstrate your code for 1 You may skip pivoting for simplicity. If you do so, it means P = I (identity matrix). 12 1 0 0 1 0 0 07 1 2 1 0 A= 0 0 B= 0 0 1 2 1 0 0 1 0 LO 0 1 2 LO 0 0 1 (Now you should realize that you have developed a program that can calculate A-7 for any invertible matrix A.) Problem 3 [4 pts]: Develop a computer program that solves matrix equation AX = B, using LU decomposition. Here A is an n x n square matrix, B is an n x m matrix. (Therefore the dimensions of the unknown matrix X is n x m.) You can use any existing function (e.g., lu(...) in MATLAB) to perform the LU decomposition on A, which will give you a permutation matrix? P, a lower triangular matrix L, and an upper triangular matrix U, such that PA = LU. But you should write your own program to solve LUX = PB, (equivalent to AX = B) taking advantage of the fact that L and U are triangular matrices. Your code should not use any built-in functions for solving linear systems or inverting a matrix. Demonstrate your code for 1 You may skip pivoting for simplicity. If you do so, it means P = I (identity matrix). 12 1 0 0 1 0 0 07 1 2 1 0 A= 0 0 B= 0 0 1 2 1 0 0 1 0 LO 0 1 2 LO 0 0 1 (Now you should realize that you have developed a program that can calculate A-7 for any invertible matrix A.)