Apply the Gauss-Seidel method to solve the following system of equations iteratively toward a guaranteed solution. Note: Use the order of u first, v next and then w to generate your solutions. u+w-8=-(u+ v) + 5w 7v+4w=7+5u+7v u+5(w+v-1)=13v-8 What are your results for u v and w after 2 iterations ? Include 4 decimal places in your answers. Save your work and submit image using file submission link. U= VE W=

Apply the Gauss-Seidel method to solve the following system of equations iteratively toward a guaranteed solution. Note: Use the order of u first, v next and then w to generate your solutions. u+w-8=-(u+ v) + 5w 7v+4w=7+5u+7v u+5(w+v-1)=13v-8 What are your results for u v and w after 2 iterations ? Include 4 decimal places in your answers. Save your work and submit image using file submission link. U= VE W=

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Simplify the following Boolean functions, using Karnaugh maps: a. F(w, x, y, z) = E(0,2,3,8,10,11) b. F(A, B,C, D) = E(1,5,9,12,13,15) %3D
Given the following system of equations, create a code in Matlab (or other software) using the Gauss-Seidel method to solve with 10 iterations. Make a graph of solutions vs number of iterations and estimate from what iteration begins to converge to the solution.
2. Consider the Karnaugh map of a Boolean function k(w, x, y, z) shown at right. I (a) Use the Karnaugh map to find the DNF for k(w, x, y, z). (b) Use the Karnaugh map algorithm to find the minimal expression for k(w, x, y, z). x y z h(x, y, z) 0 0 1111OOOO: 0 0 0 0 нноонно 10 1 1 LOLOLOL 3. Use a don't care Karnaugh map to find a minimal representation for a Boolean expression h(x,y,z) agreeing with the incomplete I/O table below: 1 0 0 0 1 OLO 0 0 NE IN xy yz 1 IN WX yz 1 ÿz 1 wx wx wox xy xy fy 1 1 1 1
A given system of linear equations Ax = b can be solved using Gaussian elimination. For the following A's and b's, perform as indicated: Problem 1: (3 1 2 A1 = 4 2 8 2 4 4. xv1= y b1 = 1 Problem 2: 12 1 2 3 3 4 x1 x2 Xv2= x3 A2 = b= 0 3 3 0 2 1 -4. x4 Script e H Save C Reset I MATLAB Documentation 1 %Encode A1, b1 and x1 as the vector of unknowns. 2 A1 = 3 b1 = 4 syms 5 xv1 = 6 7 %Check the size of A, set it as m1 and n1 8 [m1, n1] - 9 10 %Augment A and b to form AM1 11 AM1 = 12 13 %Solve the Reduced Rwo Echelon of AM1. 14 RREFA1 = 15 16 %Collect the last column and set as bnew1, set the remaining elements as Anew1 17 bnew1= 18 Anew1 = 19 20 %Check if Anew is an identity matrix, if it is, bnew is the solution 21 if Anew1 =eye(m1, n1) 22 Root1 - bnew1 23 else 24 display("No Solution") 25 end 26
A simple pendulum of length L, has a maximum angular displacement e_max. At one point in its motion, its kinetic energy is K = 3 J and its potential energy is U = 4.2 J. When the pendulum's angular velocity is one-fourth its maximum value (0' = %3D O'_max/4), then its kinetic energy is:
The electric flux density D at the point M (0,4,0) in the region about a uniform line charge of 1 nC/m lying along the z axis in free space is: Select one: a. None of the above b. 0.6366 nC/m c. 0.2387 nC/m d. 0.039 nC/m e. 0.1 nC/m
A discharge factor is a ratio which compares the mass flow rate at the end of a channel or nozzle to an ideal channel or nozzle. The discharge factor for flow through an open channel of parabolic cross-section is: K = 1.2 [V16x +1+ In(V16x² +1+4x)]³ 4x where x is the ratio of the maximum water depth to breadth of the channel at the top of the water. Determine the discharge factors for x in the range 0.45 to 0.90 in steps of 0.05. Script e C Reset I MATLAB Docume 1 %Give values for x: 2 3 %Solve for K: 4
The van der Waal's equation of state is given as RT a v-b v² For sulfur dioxide at temperature, T, of 300 K and a pressure, P, of 1 atm, the constants are given as: R = 0.08206 L.atm/(mol.K) L2.mol² P = a = 6.7689 atm.L b=0.05679 L.mol™¹ a) Plot the function f(v)=0 the for volumes for the range of 0 to 40 L/mol using 0.5 increment. b) Identify the root in this plot (where the curve crosses x-axis). c) Use the MATLAB function (fzero) to solve the original f(v) function for the specific volume using the initial guess from part (c). d) Use the MATLAB function (roots) to solve the original f(v) function for the specific volume.
Simplify the following Boolean functions, using three-variable Kmaps: F(x, y, z)=Σ(3, 4, 5, 6, 7)
Given the following Boolean function: F (w, , Y, z) = E (2, 3, 6, 7, 8, 9, 12, 13) Reduce it to its minimal/simplest expression using ONLY Boolean algebra postulates and theorems.
When purifying drinking water you can use a so-called membrane filtration. In an experiment one wishes to examine the relationship between the drop across a membrane and the flux (flow per area) through the membrane. We observe the following 10 related values of pressure (x) and flux (y): pressure 2 3 4 5 6 7 8 9. 10 Pressure (x) 1.02 2.08 2.89 4.01 5.32 5.83 7.26 7.96 9.11 9.99 Flux (y) 1.15 0.85 1.56 1.72 4.32 5.07 5.00 5.31 6.17 7.04 Copy this into R to avoid typing in the data: D <- data.frame( pressure=c(1.02,2.08,2.89,4.01,5.32,5.83,7.26,7.96,9.11,9.99), flux=c(1.15,0.85,1.56,1.72,4.32,5.07,5.00,5.31,6.17,7.04)
Solve by MATLAB