Please Code in Matlab

Let A be an n x n matrix and b a column vector with n entries. There are a number of ways to solve the linear system Ac = b. Here are some: I = A-1 (if A is invertible). The MATLAB command to invert a matrix is inv. I =A\6. Note that is a MATLAB operator. You can refer to this method as the "built-in solver." Compute the LU decomposition of A=LU. Solve y = L\b and then r = U\y. The MATLAB command to compute L and U is lu. You are going to look at the efficiency in terms of computation time) of each of these methods to solve a linear system, using random n x n square matrices of large size. Below are the precise instructions of what needs to be done: 1. We want to consider values of n ranging from n = 100 to n = 1000, with increments of 50. Requirement: use the construction a:b:c to generate this range of values of n and use a for loop to iterate through this range of values of n. 1 2. For each value of n we want to generate 10 random linear systems with floating point coefficients between 0 and 1. Each system will be described by an n x n random matrix A and a random column vector b of size n, both filled with floating point numbers between 0 and 1. Use the command rand for this. 3. For each such system, solve the system with the three methods described above, and for each method record the time it took to solve the system. To record the time, use the commands tic and toc. 4. For each method plot a graph of how long the computation takes as a function of n, averaged over the 10 random systems generated for each value of n. The MATLAB command to plot these graphs is plot. To give a title and labels to the axes, use title, xlabel, ylabel. Plot all three graphs in the same figure, and use legend to label each of them. Use solid, dashed and dash-dot lines for the three graphs. 5. Once you have the results and have plotted them, please comment briefly in your document about how the three methods behave in terms of computation time