document.write( "Question 1136394: (a) Consider the following system of linear equations:
\n" ); document.write( "x + 5y + z = 0
\n" ); document.write( "x + 6y − z = 0
\n" ); document.write( "2x + ay + bz = c
\n" ); document.write( "Find values of a, b, and c such that the above system of linear equations has:
\n" ); document.write( "(i) exactly one solution;
\n" ); document.write( "(ii) an infinite number of solution;
\n" ); document.write( "(iii) no solution; \n" ); document.write( "

Algebra.Com's Answer #754176 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Add the first and the second equations. You will get\r\n" );
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document.write( "2x + 11y +0*z = 0.    (4)\r\n" );
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document.write( "The third equations is\r\n" );
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document.write( "2x +  ay + b*z = c    (3)\r\n" );
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document.write( "Comparing (3) and (4), you can conclude:\r\n" );
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document.write( "(iii)  if a= 11,  b= 0 and c is any nonzero number, then the given system has no solution.\r\n" );
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document.write( "{ii)   if a= 11, b= 0 and c= 0, then the system has infinitely many solutions.\r\n" );
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document.write( "(i)    if a= 11, b=/= 0 then the system has a unique solution for any value of c.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that the problem asks to find the value \"a\", \"b\" and \"c\" satisfying some conditions - and I found such values \"a\", \"b\" and \"c\".\r
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\n" ); document.write( "\n" ); document.write( "The problem does not require to find ALL values of \"a\", \"b\" and \"c\", satisfying the given requirements.\r
\n" ); document.write( "\n" ); document.write( "Therefore, I even didn't try answer this EXTENDED question.\r
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