Question 1080855
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<pre>
<U>Solution 1</U>


1.  Find the determinant det(M) of the 3x3-coefficient matrix M.
    The determinant depends on parameter A.
    More exactly, the determinant is a linear function of the parameter A.
    The necessary condition for the system to be inconsistent is det(M) = 0.
     
2.  Solve this equation det(M) = 0 for A and find its roots.


3.  The condition det(M) = 0 is the necessary, but still not the sufficient condition for the system to be inconsistent.


4.  So, you need to check for the found value of A whether the system has a solution or no.

    But with the found value of A, the system is simply with numerical coefficients.
    It just does not contain the parameter.
    It contain only numerical coefficients.
</pre>

This is the plan.
Unfortunately, I don't know your grade and your level of knowledge in the subject.
But my question is: Do you understand this plan?
Are you ready to follow it ?
Do you understand what to do?



There is <U>another way</U>, <U>more easy, in my view</U>.



<U>Solution 2</U>


<pre>
1.  By adding and subtracting equations, eliminate "x" from the system and reduce the given 3x3-system in 3 unknowns 
    to 2x2-system in 2 unknowns "y" and "z".

    The matrix still will contain the parameter A, but it will be only 2x2-matrix.


2.  Starting from this point, you need to make the same steps as in the <U>Solution 1</U>.

    But this time for 2x2-matrix instead of the original 3x3-matrix, which is MUCH easier.
</pre>

Please feel free to write me your feedback. 


If you need more help, let me know via the "Thank you" message.


But I need to know what is your grade and what is your level of knowledge in the subject.

<pre>
    Do you know the Elimination method ?
    Do you know the Substitution method ?
    Do you know the Determinant method ?
    Do you know what the determinant is and how to calculate it ?
    Do you know criterions for a matrix equation to be consistent/inconsistent/dependent ?
    Do you know the Cramer's rule ?
</pre>

It doesn't seem to be a school problem, isn't it?  
Am I right ?


Is this the college problem ?


I need to know with whom and for whom I work . . . 


Actually, this site <A HREF=www.algebra.com>www.algebra.com</A> contains lessons that cover all the positions listed above,
and if I see the wishing and the desire from your side to learn it, I can give you the list of lessons.



Good luck !!