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- Solve the system of linear equation: -5x + 4y = -1 8x - 7y = -7 2x - 9y = -6 Apply the algebra matrix through 1 direct and 1 iterative method. The use of the inverse method is not allowed. Kindly add comments on the MATLAB code so the code would be understandable. Thank you!Draw the PNR (Putnam-Nordan-Rayleigh) curve. What information can be obtained from it?Given two objects represented by the tuples (25, 5, 52, 14) and (10, 0, 36, 8):(a) Compute the Euclidean distance between the two objects.(b) Compute the Manhattan distance between the two objects.(c) Compute the Minkowski distance between the two objects, using q=3
- 1. Suppose that we have four observations and compute a dissimilarity matrix given by 0.3 0.3 0.4 0.7 0.5 0.8 0.4 0.5 0.45 0.7 0.8 0.45 For instance, the dissimilarity between the first and second observations is 0.3, and the dissim- ilarity between the second and fourth observations is 0.8. (a) On the basis of this dissimilarity matrix, sketch the dendrogram that results from hierar- chically clustering these four observations using complete linkage. Be sure to indicate on the plot the height at which each fusion occurs, as well as the observations corresponding to each leaf in the dendrogram. (b) Repeat (a), this time using single linkage clustering. (c) Suppose that we cut the dendrogram obtained in (a) such that two clusters result. Which observations are in each cluster? (d) Suppose that we cut the dendrogram obtained in (b) such that two clusters result. Which observations are in each cluster?Boolean function is represented by its truth table as follows: хуz f(x,y,z) 000 1 001 1 010 011 100 101 1 110 111 1 (a) Write corresponding minterm expansion. (b) Write corresponding maxterm expansion. (c) Minimize (Simplify) and Represent f(x,y,z) using Karnaugh map (K-map). (d) Minimize (Simplify) f(x,y,z) using Boolean identities. (e) Represent the simplified function using logic diagram.Please explain, as simplistically (but thoroughly) as possible, how to develop a k-map from a truth table to be used to simplify an equation.Examples: xz + (xy + ~z) ~xyz + yz + x~y
- As we showed, the horizontal displacements ξi of masses i = 1 . . . N satisfy equations of mo- tion md2ξ1 =k(ξ2−ξ1)+F1, dt2 md2ξi =k(ξi+1−ξi)+k(ξi−1−ξi)+Fi, dt2 md2ξN =k(ξN−1−ξN)+FN. dt2 where m is the mass, k is the spring constant, and Fi is the external force on mass i. In Exam- ple 6.2 we showed how these equations could be solved by guessing a form for the solution and using a matrix method. Here we'll solve them more directly. a) Write a python program to solve for the motion of the masses using the fourth-order Runge- Kutta method for the case we studied previously where m = 1 and k = 6, and the driving forces are all zero except for F1 = cos ωt with ω = 2. Plot your solutions for the displace- mentsξi ofallthemassesasafunctionoftimefromt=0tot=20onthesameplot. Write your program to work with general N, but test it out for small values—N = 5 is a reasonable choice. You will need first of all to convert the N second-order equations of motion into 2N first- order equations.…Assume that W is a standard Brownian motion. Explain how to simulate (W1/2, W1) using at least two methods.Use Cholesky factorization and find the matrix satisfying it. Please use matlab software to answer it and attach the simulation with the code.
- Given two particles with Q = 4.30-µC charges as shown in the figure below and a particle with charge q = 1.39 x 10-18 C at the origin. (Note: Assume a reference level of potential V = 0 at r = co.) x = -0.800 m x = 0.800 m (a) What is the net force (in N) exerted by the two 4.30-µC charges on the charge q? (Enter the magnitude.) N (b) What is the electric field (in N/C) at the origin due to the two 4.30-pC particles? (Enter the magnitude.) V N/C (c) What is the electrical potential (in kV) at the origin due to the two 4.30-uC particles? 96.75 V kV (d) What If? What would be the change in electric potential energy (in J) of the system if the charge g were moved a distance d = 0.400 m closer to either of the 4.30-µC particles?vVrite a matlab program to display the eigen matrix, transpose, inverse of a given matrixI need help with my MATLAB code. I am using ode45 to solve my differential equation. But, the size of w_ode is 9x645. Size of t is also 1x645. How is that possible? Shouldn't t be 1x101 and w_ode be 9x101? How do I get the size to be 9x101? I need that size because I am subtract that matrix by another matrix of the same size. I_T = 2;J = 1.5;I = [I_T; I_T; J];w = [-0.1; 0.3; -1.1];L = [0;0;0]; t = 0:100; % Using ode45 to integrate w dotoptions = odeset('RelTol',1e-10,'AbsTol',1e-10);result = ode45(@dwdt_Bframe, t, [w; I; L], options); % Extracting information from ode solvert = result.xw_ode = result.y function dwdt = dwdt_Bframe(t, wIL) w = wIL(1:3); I = wIL(4:6); L = wIL(7:9); % The w dot equations dwdt = zeros(9,1); dwdt(1) = (-(I(3) - I(2))*w(2)*w(3) + L(1)) / I(1); dwdt(2) = (-(I(1) - I(3))*w(3)*w(1) + L(2)) / I(2); dwdt(3) = (-(I(2) - I(1))*w(1)*w(2) + L(3)) / I(3); % Keep the values of I and L constant dwdt(4:6) = 0; dwdt(7:9) = 0; end