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If one of your equations becomes the true statement 0 = 0 during Gaussian Elimination, that means your system could have infinitely many ordered triple solutions. True False

If one of your equations becomes the true statement 0 = 0 during Gaussian Elimination, that means your system could have infinitely many ordered triple solutions. True False

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Gaussian Elimination and System of Equations** --- If one of your equations becomes the true statement 0 = 0 during Gaussian Elimination, that means your system could have infinitely many ordered triple solutions. * True ○ * False ○ --- **Understanding Gaussian Elimination:** Gaussian Elimination is a method used to solve systems of linear equations. It transforms the system into an upper triangular matrix and then uses back substitution to find the solution. *Important Concept:* - When simplifying a system of equations using Gaussian Elimination, encountering an equation that simplifies to 0 = 0 indicates that the system is potentially dependent, leading to infinitely many solutions. This situation typically arises in a system where there are more variables than independent equations, resulting in a dependent system. **Visual Aids:** - There are no graphs or diagrams provided in the image. Ensure you comprehend the implication of each step in your solution process when using Gaussian Elimination to analyze systems of equations. Do you have any questions or need further clarification on this topic? Feel free to ask!
Transcribed Image Text:**Gaussian Elimination and System of Equations** --- If one of your equations becomes the true statement 0 = 0 during Gaussian Elimination, that means your system could have infinitely many ordered triple solutions. * True ○ * False ○ --- **Understanding Gaussian Elimination:** Gaussian Elimination is a method used to solve systems of linear equations. It transforms the system into an upper triangular matrix and then uses back substitution to find the solution. *Important Concept:* - When simplifying a system of equations using Gaussian Elimination, encountering an equation that simplifies to 0 = 0 indicates that the system is potentially dependent, leading to infinitely many solutions. This situation typically arises in a system where there are more variables than independent equations, resulting in a dependent system. **Visual Aids:** - There are no graphs or diagrams provided in the image. Ensure you comprehend the implication of each step in your solution process when using Gaussian Elimination to analyze systems of equations. Do you have any questions or need further clarification on this topic? Feel free to ask!
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