Solving Matrix Help: Find Values of k w/o Solution

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Homework Help Overview

The discussion revolves around determining the values of k for which a given system of equations represented by a matrix does not have a solution. The subject area is linear algebra, specifically focusing on matrix operations and properties related to solutions of systems of equations.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants suggest performing matrix operations to express variables in terms of k, and discuss the implications of having a row that leads to a contradiction. Others mention the relevance of the determinant being zero as a condition for the system to lack a unique solution.

Discussion Status

The discussion is active, with various approaches being explored. Some participants provide guidance on manipulating the matrix and interpreting the results, while others clarify the distinction between having no solution and having no unique solution.

Contextual Notes

There are repeated requests for clarification on the problem, indicating potential confusion or lack of information regarding the matrix setup or the values of k being considered.

Coolies
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Matrix Help! ahhh

http://img152.imageshack.us/img152/9982/matrixnq8.gif

What values of k does the system not have a solution?

I don't know how to do this question. Anybody have any ideas? :)
 
Last edited by a moderator:
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Perform a matrix operation to one of the rows so that you can solve for one of the variables, in terms of k. What i would do is eliminate the 1 from the bottom row, so that it is of the form:

[ 0 f(k) g(k) ]

Then use the fact that if 0x = c (where c is some non zero constant), then the equation cannot be solved.
 
Another way to do this is when the determinant of the matrix is zero, then this system of equations has no solution.
 
Coolies said:
http://img152.imageshack.us/img152/9982/matrixnq8.gif

What values of k does the system not have a solution?

I don't know how to do this question. Anybody have any ideas? :)
Yes: try and solve the system.
 
Last edited by a moderator:
malawi_glenn said:
Another way to do this is when the determinant of the matrix is zero, then this system of equations has no solution.

You mean no unique sol'n. This is for the op's knowledge.
 

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