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3w + 2x – 8y = -5 Ow + 9x +4y + 3z = 4 – 13w + 2x + 6y +z = -7 - 2w + 3x + 2y + 10z = 0 SECTION I: DIRECT METHODS IN SOLVING SYSTEMS OF LINEAR EQUATIONS 1. Find the solution of the system of linear equation using GAUSS-JORDAN ELIMINATION. If the results are not reducible to fractions, write the values up to 6 decimal places.

3w + 2x – 8y = -5 Ow + 9x +4y + 3z = 4 – 13w + 2x + 6y +z = -7 - 2w + 3x + 2y + 10z = 0 SECTION I: DIRECT METHODS IN SOLVING SYSTEMS OF LINEAR EQUATIONS 1. Find the solution of the system of linear equation using GAUSS-JORDAN ELIMINATION. If the results are not reducible to fractions, write the values up to 6 decimal places.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 1CEXP
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Follow up for section 3:
Stopping criterion: Absolute error
e=0.00001
The Augmented matrix is as follows: 3 2 -8 -1 -5 9. 4 3 4 -13 2 6. 1 1 -7 -2 3 2 10 | 0 in equation form 3w + 2x - 8y -z = -5 Ow + 9x + 4y + 3z = 4 - 13w + 2x + 6y +z = -7 - 2w + 3x + 2y + 10z = 0 %3D SECTION I: DIRECT METHODS IN SOLVING SYSTEMS OF LINEAR EQUATIONS 1. Find the solution of the system of linear equation using GAUSS-JORDAN ELIMINATION. If the results are not reducible to fractions, write the values up to 6 decimal places. 2. Solve the same system using Cramer's Rule. The Augmented matrix is as follows: -13 2 6. 1|-7 9. 4 3 4 3 2 -8 -1|-5 -2 3 10 | 0 in equation form - 13w + 2x +6y +z = -7 Ow + 9x +4y + 3z = 4 Зw + 2x — 8у —z 3D —5 -z = -5 - 2w + 3x + 2y + 10z = 0 SECTION II : ITERATIVE METHODSS IN SOLVING SYSTEMS OF LINEAR EQUATIONS 1. Find the solution of the system of linear equation using JACOBI ITERATION. STOP at the 5th Iteration. Compute the ABSOLUTE ERROR for each iteration. Show the working equation and write the solution for each iteration very clearly. If the results are not reducible to fractions, write the values up to 6 decimal places. 2. Find the solution of the system of linear equation using GAUSS-SEIDEL ITERATION. STOP at the 5th Iteration. Compute the ABSOLUTE ERROR for each iteration. Show the working equation and write the solution for each iteration very clearly. If the results are not reducible to fractions, write the values up to 6 decimal places. SECTION II: SOLUTIONS TO NONLINEAR-EQUATIONS 2 sin(e*) f(x) 1. Given f(x) above, find f'(x). 2. Between the interval [1,2] find the two roots of the function using NEWTON- RHAPSON Method. a. Use x,=1 as initial quess #1. b. Use xo=2 as initial guess #2. Use RADIANS MODE in your calculators when solving this problem. F(r) = 2 in(@")
Transcribed Image Text:The Augmented matrix is as follows: 3 2 -8 -1 -5 9. 4 3 4 -13 2 6. 1 1 -7 -2 3 2 10 | 0 in equation form 3w + 2x - 8y -z = -5 Ow + 9x + 4y + 3z = 4 - 13w + 2x + 6y +z = -7 - 2w + 3x + 2y + 10z = 0 %3D SECTION I: DIRECT METHODS IN SOLVING SYSTEMS OF LINEAR EQUATIONS 1. Find the solution of the system of linear equation using GAUSS-JORDAN ELIMINATION. If the results are not reducible to fractions, write the values up to 6 decimal places. 2. Solve the same system using Cramer's Rule. The Augmented matrix is as follows: -13 2 6. 1|-7 9. 4 3 4 3 2 -8 -1|-5 -2 3 10 | 0 in equation form - 13w + 2x +6y +z = -7 Ow + 9x +4y + 3z = 4 Зw + 2x — 8у —z 3D —5 -z = -5 - 2w + 3x + 2y + 10z = 0 SECTION II : ITERATIVE METHODSS IN SOLVING SYSTEMS OF LINEAR EQUATIONS 1. Find the solution of the system of linear equation using JACOBI ITERATION. STOP at the 5th Iteration. Compute the ABSOLUTE ERROR for each iteration. Show the working equation and write the solution for each iteration very clearly. If the results are not reducible to fractions, write the values up to 6 decimal places. 2. Find the solution of the system of linear equation using GAUSS-SEIDEL ITERATION. STOP at the 5th Iteration. Compute the ABSOLUTE ERROR for each iteration. Show the working equation and write the solution for each iteration very clearly. If the results are not reducible to fractions, write the values up to 6 decimal places. SECTION II: SOLUTIONS TO NONLINEAR-EQUATIONS 2 sin(e*) f(x) 1. Given f(x) above, find f'(x). 2. Between the interval [1,2] find the two roots of the function using NEWTON- RHAPSON Method. a. Use x,=1 as initial quess #1. b. Use xo=2 as initial guess #2. Use RADIANS MODE in your calculators when solving this problem. F(r) = 2 in(@")
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