Linear Algebra, forcing a row exchange.

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SUMMARY

The discussion centers on the concept of row exchanges in linear algebra, specifically regarding a system of equations that maintains an upper triangular form. The key point raised is that the value of d, which the answer key indicates should be 10, can be manipulated to avoid a row exchange. The participants emphasize that while the system can be solved in various ways, adhering to an upper triangular structure imposes specific constraints on the value of d that necessitate a row exchange.

PREREQUISITES
  • Understanding of upper triangular matrices
  • Familiarity with systems of linear equations
  • Knowledge of row operations in linear algebra
  • Basic concepts of matrix manipulation
NEXT STEPS
  • Research the implications of row exchanges in upper triangular matrices
  • Study the methods for solving systems of equations without enforcing triangular forms
  • Explore the concept of pivoting in Gaussian elimination
  • Learn about the conditions that lead to row exchanges in matrix operations
USEFUL FOR

Students and educators in mathematics, particularly those focusing on linear algebra, as well as anyone interested in advanced matrix manipulation techniques.

Terrell
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the answer key said d is supposed to be 10. but there's a way to evade that row exchange. 1st picture is the question and the 2nd picture is the elimination steps.
 

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I think that the question is asking which value of d "forces" a row exchange if you keep it upper triangular. In general, the system of equations can be solved in many ways if you don't insist on keeping an upper triangular form.
 
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FactChecker said:
I think that the question is asking which value of d "forces" a row exchange if you keep it upper triangular. In general, the system of equations can be solved in many ways if you don't insist on keeping an upper triangular form.
good point!
 

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