Is the given system of equations solvable with back substitution?

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Homework Help Overview

The discussion revolves around the solvability of a system of equations involving five variables and three equations. Participants are examining the implications of the number of equations relative to the number of variables.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants suggest that the lack of equations compared to variables indicates no solution, while others question the interpretation of the final row of the augmented matrix as an equation. There is also exploration of the implications of having multiple variables and equations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the equations and the conditions under which solutions may exist. There is no explicit consensus, but various perspectives on the nature of the solutions are being shared.

Contextual Notes

Participants are considering the implications of having three equations for five unknowns, and the potential for different types of solutions based on the structure of the equations presented.

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Homework Statement



I have attached the question

Homework Equations





The Attempt at a Solution



I think the answer is no solution because there is 5 variables but only 3 equations. Is that correct?
 

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TyErd said:

Homework Statement



I have attached the question

Homework Equations





The Attempt at a Solution



I think the answer is no solution because there is 5 variables but only 3 equations. Is that correct?

No, that is not the reason. Look at the final row; it is shorthand for an equation involving x1, x2, x3, x4, x5. What is the equation?

RGV
 
do you mean 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4?
 
if the third is also an equation that means there must be an answer right? So because we have to assign variables and we have 5unknowns and 3 equations that must mean two values will be variables right?? so the answer has to be B yeah??
 
TyErd said:
do you mean 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4?
For what values of the variables x1, x1, x2, x3, and x4 will this be a true statement?


TyErd said:
if the third is also an equation that means there must be an answer right?
Not necessarily. There are three possibilities for a system of equations (which are here represented by an augmented matrix):
1) a unique solution
2) multiple solutions
3) no solution.
TyErd said:
So because we have to assign variables and we have 5unknowns and 3 equations that must mean two values will be variables right?? so the answer has to be B yeah??
 

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