Please solve using Matlab

Problem 1: Poisson's Equation Consider the linear system Anp-p, where An is an n x n matrix with 2's on the main diagonal, -1's directly above and below the main diagonal and 0's everywhere else. For example, A5 is 2-1 0 0 0 1 2-1 0 0 A50 -1 2-1 0 0 0 -1 2-1 0 0 0-1 2 This is a discretized version of Poisson's equation d'p(x) which appears very often in physical applications. We will discuss discretizations and differential equations, including the origin of this matrix An, later in the class Construct the matrix A75 in Matlab. (Look at the help file for the diag command; you can make this matrix with just a few lines of code.) In addition, make the 75 x 1 vector such that the jth entry of is defined according to the formula 21Tj 76 S H - COS_ 76 (a) The Jacobi iteration method for this problem can be written as Ok-MOk-itc (Note that .k means the kth guess for , and it is an entire vector. It does not mean the kth entry of .) Find the largest (in magnitude) eigenvalue of M and save the magnitude of this eigenvalue in A1.dat. (b) Use Jacobi iteration to solve for . Your initial guess should be a 75 1 vector of all ones, and you should use a tolerance of 10-4. That is, you should stop when Problem 1: Poisson's Equation Consider the linear system Anp-p, where An is an n x n matrix with 2's on the main diagonal, -1's directly above and below the main diagonal and 0's everywhere else. For example, A5 is 2-1 0 0 0 1 2-1 0 0 A50 -1 2-1 0 0 0 -1 2-1 0 0 0-1 2 This is a discretized version of Poisson's equation d'p(x) which appears very often in physical applications. We will discuss discretizations and differential equations, including the origin of this matrix An, later in the class Construct the matrix A75 in Matlab. (Look at the help file for the diag command; you can make this matrix with just a few lines of code.) In addition, make the 75 x 1 vector such that the jth entry of is defined according to the formula 21Tj 76 S H - COS_ 76 (a) The Jacobi iteration method for this problem can be written as Ok-MOk-itc (Note that .k means the kth guess for , and it is an entire vector. It does not mean the kth entry of .) Find the largest (in magnitude) eigenvalue of M and save the magnitude of this eigenvalue in A1.dat. (b) Use Jacobi iteration to solve for . Your initial guess should be a 75 1 vector of all ones, and you should use a tolerance of 10-4. That is, you should stop when