document.write( "Question 1080855: 4x-12y-8z=A^2
\n" ); document.write( "8x-20y+Az=36
\n" ); document.write( "8x-32y+4z=72
\n" ); document.write( "Find all values of A For which the system has no solution.
\n" ); document.write( "Please help, can you offer step by step so I understand how to do it? \n" ); document.write( "

Algebra.Com's Answer #694933 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Solution 1\r\n" );
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document.write( "1.  Find the determinant det(M) of the 3x3-coefficient matrix M.\r\n" );
document.write( "    The determinant depends on parameter A.\r\n" );
document.write( "    More exactly, the determinant is a linear function of the parameter A.\r\n" );
document.write( "    The necessary condition for the system to be inconsistent is det(M) = 0.\r\n" );
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document.write( "2.  Solve this equation det(M) = 0 for A and find its roots.\r\n" );
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document.write( "3.  The condition det(M) = 0 is the necessary, but still not the sufficient condition for the system to be inconsistent.\r\n" );
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document.write( "4.  So, you need to check for the found value of A whether the system has a solution or no.\r\n" );
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document.write( "    But with the found value of A, the system is simply with numerical coefficients.\r\n" );
document.write( "    It just does not contain the parameter.\r\n" );
document.write( "    It contain only numerical coefficients.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This is the plan.
\n" ); document.write( "Unfortunately, I don't know your grade and your level of knowledge in the subject.
\n" ); document.write( "But my question is: Do you understand this plan?
\n" ); document.write( "Are you ready to follow it ?
\n" ); document.write( "Do you understand what to do?\r
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\n" ); document.write( "\n" ); document.write( "There is another way, more easy, in my view.\r
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\n" ); document.write( "\n" ); document.write( "Solution 2\r
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document.write( "1.  By adding and subtracting equations, eliminate \"x\" from the system and reduce the given 3x3-system in 3 unknowns \r\n" );
document.write( "    to 2x2-system in 2 unknowns \"y\" and \"z\".\r\n" );
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document.write( "    The matrix still will contain the parameter A, but it will be only 2x2-matrix.\r\n" );
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document.write( "2.  Starting from this point, you need to make the same steps as in the Solution 1.\r\n" );
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document.write( "    But this time for 2x2-matrix instead of the original 3x3-matrix, which is MUCH easier.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Please feel free to write me your feedback. \r
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\n" ); document.write( "\n" ); document.write( "If you need more help, let me know via the \"Thank you\" message.\r
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\n" ); document.write( "\n" ); document.write( "But I need to know what is your grade and what is your level of knowledge in the subject.\r
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document.write( "    Do you know the Elimination method ?\r\n" );
document.write( "    Do you know the Substitution method ?\r\n" );
document.write( "    Do you know the Determinant method ?\r\n" );
document.write( "    Do you know what the determinant is and how to calculate it ?\r\n" );
document.write( "    Do you know criterions for a matrix equation to be consistent/inconsistent/dependent ?\r\n" );
document.write( "    Do you know the Cramer's rule ?\r\n" );
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\n" ); document.write( "\n" ); document.write( "It doesn't seem to be a school problem, isn't it?
\n" ); document.write( "Am I right ?\r
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\n" ); document.write( "\n" ); document.write( "Is this the college problem ?\r
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\n" ); document.write( "\n" ); document.write( "I need to know with whom and for whom I work . . . \r
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\n" ); document.write( "\n" ); document.write( "Actually, this site www.algebra.com contains lessons that cover all the positions listed above,
\n" ); document.write( "and if I see the wishing and the desire from your side to learn it, I can give you the list of lessons.\r
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\n" ); document.write( "\n" ); document.write( "Good luck !!\r
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