Solve this simple simultaneous linear equation using Gauss elimination method and Gauss-Jordan method: 2x2 + 3x3 = 8 4.x1 + 6x2 + 7xz = -3 %3D 2x1 – 3x2 + 6x3 = 5

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 2BEXP
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please solve that question with calculation, without use matlab

tq

where Qg and Q̟ are the gas and liquid flow rates, respec-
tively, and D = the gas-liquid exchange rate. Similar balances
can be written for the other reactors. Use Gauss-Seidel with-
out relaxation to solve for the concentrations given the fol-
lowing values: Qg=2, QL = 1, D=0.8, cG0 = 100,
CL6 = 10.
\Qg_
C G5
CG2
CG3
D
CLA
CL5
• C 16
CLI
C 12
CL3
Transcribed Image Text:where Qg and Q̟ are the gas and liquid flow rates, respec- tively, and D = the gas-liquid exchange rate. Similar balances can be written for the other reactors. Use Gauss-Seidel with- out relaxation to solve for the concentrations given the fol- lowing values: Qg=2, QL = 1, D=0.8, cG0 = 100, CL6 = 10. \Qg_ C G5 CG2 CG3 D CLA CL5 • C 16 CLI C 12 CL3
1.
Solve this simple simultaneous linear equation using Gauss elimination method and
Gauss-Jordan method:
2x2 + 3x3 = 8
4.x1 + 6x2 + 7x3 = -3
2x1 – 3x2 + 6x3 = 5
Use the Gauss-Seidel method to solve the following system until the percent relative
error falls below ɛs = 5%:
2.
0.8
-0.4
41
-0.4
0.8
-0.4
25
-0.4
0.8
105
3.
The following system of equations is designed to determine concentrations in a series
of coupled reactors as a function of the amount of mass input to each reactor. Solve this
problem with Jacobi method to Es = 5%:
15с1 — Зс2 — сз 3 3800
—Зс1 + 18с2 — бсз —D 1200
c2 + 12c3 = 2350
-4c1 –
Use the Gauss Elimination and Gauss-Jordon method to solve this problem, then solve
using Jacobi and Gauss-Seidel method. Compare the results and state the relative error.
Assume Gauss and Gauss-Jordon result are the exact solution for this problem:
2x – 6x2 – x3 = -38
-3x1 – x2 + 7xz = -34
-8x1 + x2 – 2x3 = -20
4.
Transcribed Image Text:1. Solve this simple simultaneous linear equation using Gauss elimination method and Gauss-Jordan method: 2x2 + 3x3 = 8 4.x1 + 6x2 + 7x3 = -3 2x1 – 3x2 + 6x3 = 5 Use the Gauss-Seidel method to solve the following system until the percent relative error falls below ɛs = 5%: 2. 0.8 -0.4 41 -0.4 0.8 -0.4 25 -0.4 0.8 105 3. The following system of equations is designed to determine concentrations in a series of coupled reactors as a function of the amount of mass input to each reactor. Solve this problem with Jacobi method to Es = 5%: 15с1 — Зс2 — сз 3 3800 —Зс1 + 18с2 — бсз —D 1200 c2 + 12c3 = 2350 -4c1 – Use the Gauss Elimination and Gauss-Jordon method to solve this problem, then solve using Jacobi and Gauss-Seidel method. Compare the results and state the relative error. Assume Gauss and Gauss-Jordon result are the exact solution for this problem: 2x – 6x2 – x3 = -38 -3x1 – x2 + 7xz = -34 -8x1 + x2 – 2x3 = -20 4.
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