The discussion revolves around determining the conditions under which a given system of equations will have a unique solution. The equations involve a parameter 'a' and are presented in both standard and matrix forms.
The discussion is ongoing, with some participants providing guidance on the use of matrix forms and Gaussian elimination. There is a question about the necessity of the right-hand side of the equations when considering the inverse, which has been affirmed by another participant.
The parameter 'a' introduces variability in the conditions for a unique solution, and the implications of this parameter are under consideration. The original poster expresses uncertainty about how to begin the problem-solving process.
UltrafastPED said:Rewrite the equation in matrix form:
1 -1 2 x 1
a -a 4 * y = 2a
1 1 a z 4
This system is has a unique solution if the matrix on the LHS has an inverse.
From your (3) it seems that you are to use Gaussian elimination:
http://en.wikipedia.org/wiki/Gaussian_elimination
Depending on how you set this up it can provide the inverse matrix and the solution.