How do you find the determinant

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    Determinant
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Homework Help Overview

The discussion revolves around finding the value of a parameter in a system of equations that leads to no solution. The subject area involves linear algebra, specifically the concept of determinants and the conditions for the existence of solutions in linear systems.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the method of using determinants to determine conditions for no solutions, with some suggesting that equating the determinant to zero is a valid approach. Others propose elimination methods to analyze the system of equations and question the phrasing of the original problem.

Discussion Status

The discussion is active, with various interpretations of the problem being explored. Some participants offer guidance on methods to analyze the system, while others raise questions about the phrasing and implications of the problem statement.

Contextual Notes

There is a noted ambiguity in the problem statement regarding the conditions under which there is no solution, as well as the potential for infinite solutions depending on other parameters. Participants are also considering the implications of linear dependence among the equations.

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http://users.on.net/~rohanlal/11Untitled.jpg
How do I find the value of a for which there will be no solution?
Do you find the determinant, equate it to 0 and solve for a?
 
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One perfectly good method would be to try to solve that system of equations by the usual "elimination" methods (I would be inclined to subtract one equation from the other) and see what values of a make it impossible to solve the equationl (For example, you can't divide by 0.)

By the way, the question (which I notice is NOT part of the copied statement) is not well phrased. The is NO value of a "for which there will be no solution". There is a value of a for which either there is no solution or there are an infinite number of solutions, depending on b.
 
by making a 1 you are making the matrix cingular because the row vectors are now linearlly dependent. I think the method you're using should work also... You would get
a-1 = 0...
 
Ry122 said:
http://users.on.net/~rohanlal/11Untitled.jpg
How do I find the value of a for which there will be no solution?
Do you find the determinant, equate it to 0 and solve for a?

Two straight lines will always intersect except if what about the lines are the same?
 
Last edited by a moderator:

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