Solve the given system of linear equations using the Gauss- Jordan Elimination.3.) 3x1 + 8x2 - x3 = -18 2x1 + x2 + 5x3 = 8 2x1 + 4x2 + 2x3 = -4See the example/ format below.. DIRECT METHOD 1: Gauss-Jordan EliminationGauss-Jordcn Elimination is an algorithm thatCan be uced to solve syctems of linear equotioninvertible matrix,and to find the inverse of anyIt relies upon three elementaryrow operationsOne Can use ona matrix:1.) Swap the positions of two of the rows.One of the rows by a nun zero scalor3-) Add or subtract the scalar multiple of onerow to onotherrow.X,X2X3-EXAMPLE:) X, + X2 + 2Xg =53X, t 2x, t Xg272, = 8x, - 2x2 + 3X2=0+3x,=D0Sol'n :X,21.8.3-2 32.0.R2-3R, D R2R2- R, R,メー 10x2 t 0メ3R2-3R, D R2RgRIャR32.-5-7-3-S.23ー3R2中 Rg2.1--71616R,-R, R,R3 R,8.R2 +5R2 7 Rz16ー1-21616R, tR2 # R,ャ Rz1612.00X, t0x2 t0x3っこ1X, = 1X2 =2X, = 1|-

The given system of equation is 3x1+8x2-x3=-182x1+x2+5x3=82x1+4x2+2x3=-4 It can be rewritten as…

Answered: Solve the given system of linear…

Solve the given system of linear equations using the Gauss- Jordan Elimination. 3.) 3x1 + 8x2 - x3 = -18 2x1 + x2 + 5x3 = 8 2x1 + 4x2 + 2x3 = -4 See the example/ format below..

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 2CEXP

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Question

Solve the given system of linear equations using the Gauss- Jordan Elimination.

3.) 3x₁ + 8x₂ - x₃ = -18
2x₁ + x₂ + 5x₃ = 8
2x₁ + 4x₂ + 2x₃ = -4

See the example/ format below..

DIRECT METHOD 1: Gauss-Jordan Elimination
Gauss-Jordcn Elimination is an algorithm that
Can be uced to solve syctems of linear equotion
invertible matrix,
and to find the inverse of any
It relies upon three elementary
row operations
One Can use on
a matrix:
1.) Swap the positions of two of the rows.
One of the rows by a nun zero scalor
3-) Add or subtract the scalar multiple of one
row to onother
row.
X,
X2
X3-
EXAMPLE:
) X, + X2 + 2Xg =5
3X, t 2x, t Xg
272
, = 8
x, - 2x2 + 3X2=0
+3x,=D0
Sol'n :
X,
2
1.
8.
3
-2 3
2.
0.
R2-3R, D R2
R2- R, R,
メー

10x2 t 0メ3
R2-3R, D R2
Rg
RI
ャR3
2.
-5
-7
-3
-S.
23ー3R2中 Rg
2.
1-
-7
16
16
R,-R, R,
R3 R,
8.
R2 +5
R2 7 Rz
16
ー1
-2
16
16
R, tR2 # R,
ャ Rz
16
1
2.
0
0
X, t0x2 t0x3っこ1
X, = 1
X2 =2
X, = 1
|-

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