EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 9, Problem 13P
Solve:
with (a) naive Gauss elimination, (b) Gauss elimination with partial pivoting, and (c) Gauss-Jordan without partial pivoting.
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2. Solve the system linear of Equation using Gauss- Jordan elimination (row operations), find the
value of x1, x2 and x3.
2X1 - 2X2 + X3 = 3
3X1 - X3 + X2 = 7
X1 - 3X2 + 2X3 = 0
For the following system, perform only the first elimination using Gaussian Elimination with partial pivoting.
b) By using Doolittle's or Cholesky Decomposition method
X1 + x2 + x3 = 1
4x1 + 3x2 – x3 = 6
3x1 + 5x2 + 3x3 = 4
Chapter 9 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 9 - (a) Write the following set of equations in matrix...Ch. 9 - A number of matrices are defined as...Ch. 9 - Three matrices are defined as...Ch. 9 - Use the graphical method to solve...Ch. 9 - 9.5 Given the system of equations
(a) Solve...Ch. 9 - 9.6 For the set of equations
(a) Compute the...Ch. 9 - Given the equations 0.5x1x2=9.51.02x12x2=18.8 (a)...Ch. 9 - Given the equations...Ch. 9 - Use Gauss elimination to solve:...Ch. 9 - Given the system of equations...
Ch. 9 - 9.11 Given the equations
(a) Solve by Gauss...Ch. 9 - Use Gauss-Jordan elimination to solve:...Ch. 9 - 9.13 Solve:
with (a) naive Gauss elimination,...Ch. 9 - 9.14 Perform the same computation as in Example...Ch. 9 - 9.15 Solve
Ch. 9 - 9.16 Develop, debug, and test a program in either...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - 9.19 Three masses are suspended vertically by a...Ch. 9 - 9.20 Develop, debug, and test a program in either...Ch. 9 - 9.21 Recall from Sec. 8.2 that determining the...
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- Q-Find the solution by using the simplex method? 1- Max Z=3X1+2X2 S. T: X1+X2 ≤ 4 X1-X2 ≤2 X1, X2 ≥0 2- MAX Z= 2X1+3X2+X3 S. T: 3X1+6X2+X3 ≤ 6 4X1+2X2+X3 ≤ 4 X1-X2+X3 ≤ 3 X1, X2,X3 20arrow_forwardProblem1: Solve the system of linear equations by each of the methods listed below. (a) Gaussian elimination with back-substitution (b) Gauss-Jordan elimination (c) Cramer's Rule 3x, + 3x, + 5x, = 1 3x, + 5x, + 9x3 = 2 5x, + 9x, + 17x, = 4arrow_forward1. Solve the following system of equation using Gaussian Elimination. -3x + 2y-6z = 6 5x + 7y - 5z = 6 x + 4y - 2z = 8 (x, y, z) = (-2,3,1) ·arrow_forward
- x^2-5x^(1/3)+1=0 Has a root between 2 and 2.5 use bisection method to three iterations by hand.arrow_forwardDetermine if the system is consistent or inconsistent. Justify your answer and find all solutions to the system of linear equations. Justification should be written on your solution paper. Transform the matrix into ROW ECHELON FORM (REF) using row operations. 2x +8y+ 6z = 20 4x+2y-2z =-2 3x-y+z = 11 Enter final answer: (x, y, z) =(arrow_forwardSolve the following linear programming problems using the simplex method. 1) Maximize Z = X1 + 2x2 + 3x3 X₁ + x2 + x3 ≤ 12 subject to 2x1 + x2 + 3x3 ≤18 X1, X2, X3 20arrow_forward
- for the following find f (-3.5) Lagrange Polynomials O -4 0.6 -3.64 1 -3 usingarrow_forwardUsing Gauss-Jordan Elimination, the inverse of 1 -1 1 2 0 [3 01 0 1 01 1 1 01 1 is equal to the above O is equal to the above [4 0 1 1 Lo 1 1/40 400arrow_forwardFor the DE: dy/dx=2x-y y(0)=2 with h=0.2, solve for y using each method below in the range of 0 <= x <= 3: Q1) Using Matlab to employ the Euler Method (Sect 2.4) Q2) Using Matlab to employ the Improved Euler Method (Sect 2.5 close all clear all % Let's program exact soln for i=1:5 x_exact(i)=0.5*i-0.5; y_exact(i)=-x_exact(i)-1+exp(x_exact(i)); end plot(x_exact,y_exact,'b') % now for Euler's h=0.5 x_EM(1)=0; y_EM(1)=0; for i=2:5 x_EM(i)=x_EM(i-1)+h; y_EM(i)=y_EM(i-1)+(h*(x_EM(i-1)+y_EM(i-1))); end hold on plot (x_EM,y_EM,'r') % Improved Euler's Method h=0.5 x_IE(1)=0; y_IE(1)=0; for i=2:1:5 kA=x_IE(i-1)+y_IE(i-1); u=y_IE(i-1)+h*kA; x_IE(i)=x_IE(i-1)+h; kB=x_IE(i)+u; k=(kA+kB)/2; y_IE(i)=y_IE(i-1)+h*k; end hold on plot(x_IE,y_IE,'k')arrow_forward
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