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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

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
Transcribed Image Text: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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