Use element-by-element Jacobi iteration to solve the system of equations Ax = b where 6 1-51 A-12 7 0-21 10 -1-2-31 2 H 10 and b = 3 2 You will be assessed on whether you've defined A and B correctly, whether the test for diagonal dominance is correct, whether one of the intermediate steps has been computed correctly, and whether the final step count and answer for x is correct. Make use of Matlab's help file to understand the functions being used. Script 1 2 %% Solving a matrix equation Ax=b using the Jacobi iterative technique. 3 % % The methods require A to be square and none of its main diagonal 4 %% elements can be zero. 5 6 A = ### 7 b = ### %% set b as a column vector 8 9 [# # #,N] = size(A); %%% M = number of rows, N = number of columns 10 if M~=N 11 error('A must be a square matrix') 12 end 13 14 %%% Test for diagonal dominance 15 %%% Check if the absolute value of the main diagonal elements is greater than 16 %%% the sum of the absolute value of the remaining terms in each row. 17 rowtest = abs(diag(A)) > sum(abs (A-diag(diag(A))),###); 18 index find (rowtest == ###); 19 if isempty (index) 20 21 22 23 end 24 disp("The matrix is not diagonally dominant.") disp("Take the results with caution.") pause(2) 25 % % The iterative process 26 x [0; 0; 0; 0; 0]; 27 xe = X 28 29 reldiff_tolerance = ###; 30 reldiff = 100; 31 k = 0; 32 % % The initial guess. %% setup another vector to store the new data %% set a tolerance of 10^-6 for the relative difference %% set reldiff arbitrarily high to begin %% to keep count of the number of iterations 33 fprintf('0, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',x(1),x(2),x(3),x(4),x(5)); 34 while ### > ### x0(1) = (b(1)-A(1,2:M)*x(2:M))/A(1,1); %% all terms are to the right for j = 2 M-1 terms] = A(j,1:j-1)*x(1:j-1); %% terms to the left of the main diagonal termsr = ###; %% terms to the right of the main diagonal x0(j) (b(j)-termsl-termsr)/A(j,j); 35 36 37 38 39 40 end 41 42 43 k = k+1; 44 x = ###3 45 if k == 10 46 x10 = ###3 47 end x0(M) = (b(M)-A(M,1:M-1)*x(1:M-1))/A(M,M); % % all terms are to the left reldiff = abs(norm(x-x0))/norm(x0); %% increment the iteration count %% overwrite the old data with the new data %% automatically store the value of x when k=10 48 fprintf("%d, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',k,x(1),x(2),x(3),x(4),x(5)); 49 end 50 xend ###; %% store the final value of x 51 kend ###;3 %% store the total number of iterations 52 53 Save CReset MATLAB Documentation ► Run Script ?

Explain the advantages and disadvantages of sharding, as well as the possible concerns.

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1. Compute the Laplace transform of the following equations via MATLAB. Tips: O First, you have to declare the symbolic variable names that you will be using via the MATLAB command syms. Use the MATLAB help to know more about this command and its syntax. o Write the function. o Perform the laplace transform on the function. Question 1: x(t) = sin(t) Question 2: x(t) = 5-et 4√3