than, Jackson, and Olivia are each asked to use Gaussian eliminationto solve a system of three linear equations in three variables, but theyeach have a different idea of how to start the problem.|-2x + y + 2z = -3-3x – y + 2z = -112x + y - z= 8thanwould addquation I toquation 3, andeplace equationThis wouldJacksonI would addequation I toequation 2 andreplace equation 2.This would eliminatevariable.OliviaI would subtractequation 2 fromequation I andreplace equation 2.This would eliminatethe z variable.iminate the xtheriable.-2x + y + 22 = -3ー× - y + 2z = II2x + y + 2z = -3-2x + y + 2z = -33x + Y- 2Z = |2x + y – z = 8x + 2y-2x + y + 2z = -3メ+ 2y2x + y- z = 8ー5x+ 4z = -14= 82y + z = 52x + y + 2z = -33x - y + 2z = -II2y + z = 5-2x + y + 2z = -3ー5x= 8+ 4z = -142x + y - z = 8Describe the similarities and differences among all three methods.Whose method is correct? Explain your reasoning.Is there a different way to begin the problem than the ones that werementioned? Justify your answer.

Given -2x+y+2z=-3 -3x-y+2z=-11 2x+y-z=8

Ethan, Jackson, and Olivia are each asked to use Gaussian elimination o solve a system of three linear equations in three variables, but they each have a different idea of how to start the problem. -2x + y + 2z = -3 -3x - y + 2z = -11 2x + y - z = 8

Ethan, Jackson, and Olivia are each asked to use Gaussian elimination o solve a system of three linear equations in three variables, but they each have a different idea of how to start the problem. -2x + y + 2z = -3 -3x - y + 2z = -11 2x + y - z = 8

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.2: Guassian Elimination And Matrix Methods

Problem 86E

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Question

than, Jackson, and Olivia are each asked to use Gaussian elimination
to solve a system of three linear equations in three variables, but they
each have a different idea of how to start the problem.
|-2x + y + 2z = -3
-3x – y + 2z = -11
2x + y - z= 8
than
would add
quation I to
quation 3, and
eplace equation
This would
Jackson
I would add
equation I to
equation 2 and
replace equation 2.
This would eliminate
variable.
Olivia
I would subtract
equation 2 from
equation I and
replace equation 2.
This would eliminate
the z variable.
iminate the x
the
riable.
-2x + y + 22 = -3
ー× - y + 2z = II
2x + y + 2z = -3
-2x + y + 2z = -3
3x + Y
- 2Z = |
2x + y – z = 8
x + 2y
-2x + y + 2z = -3
メ+ 2y
2x + y- z = 8
ー5x
+ 4z = -14
= 8
2y + z = 5
2x + y + 2z = -3
3x - y + 2z = -II
2y + z = 5
-2x + y + 2z = -3
ー5x
= 8
+ 4z = -14
2x + y - z = 8
Describe the similarities and differences among all three methods.
Whose method is correct? Explain your reasoning.
Is there a different way to begin the problem than the ones that were
mentioned? Justify your answer.

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