Algebra.Com's Answer #149504 by Edwin McCravy(20059)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
Hi. I am trying to make a determinant problem for someone I am tutoring. I would like something similar to the following problem that requires factoring in the result, the answer to this problem is 5/3 and -1. I am not sure how to reverse a problem to make the answer something similar to this example. Thanks to anyone who can help.\r
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document.write( "Here is the example I am trying to simulate:\r
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document.write( "  = -3
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document.write( "Here's how to make as many of them as you like. \r\n" );
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document.write( "1. Choose any integer that you want to be one of\r\n" );
document.write( "the values of x, the solution to the problem.\r\n" );
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document.write( "I'll arbitrarily choose x=2\r\n" );
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document.write( "2. Choose any two multiples of that number, positive or negative. \r\n" );
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document.write( "I'll choose two arbitrary multiples of 2, as 6 and 8.\r\n" );
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document.write( "3. Make up any determinant that contains those two multiples such\r\n" );
document.write( "that neither is in the same row or column as the other. Evaluate \r\n" );
document.write( "the determinant.\r\n" );
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document.write( " = 14\r\n" );
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document.write( "Notice I put the 6 in the 3rd row 2nd column position\r\n" );
document.write( "and the 8 in the 1st row 3rd column position, and I\r\n" );
document.write( "evaluated the determinant as 14.\r\n" );
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document.write( "Since x=2, now all I have to do is replace the 6 by 2x and \r\n" );
document.write( "the 8 by 4x\r\n" );
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document.write( " = 14\r\n" );
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document.write( "If you evaluate the determinant you get:\r\n" );
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document.write( "Divide through by 8\r\n" );
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document.write( "So there are two solutions,\r\n" );
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document.write( " and  \r\n" );
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document.write( "You can even have more fun with that determinant because \r\n" );
document.write( "it has a 4 and a -2. The 4 is 2x and the -2 is -x.\r\n" );
document.write( "So you can replace them too. Like this: \r\n" );
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document.write( " = 14\r\n" );
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document.write( "However make sure you don't have x's so as to give a \r\n" );
document.write( "third degree equation. Always leave one row or column \r\n" );
document.write( "without any unknowns. I chose to leave the first column \r\n" );
document.write( "without unknowns, Notice if had put an x where the\r\n" );
document.write( "2 is in the 2nd row 1st column, it would have resulted in\r\n" );
document.write( "a cubic equation.\r\n" );
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document.write( "But as it is, the equation comes out\r\n" );
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document.write( "So there are two solutions here, and  \r\n" );
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document.write( "It's interesting that even though was the same in\r\n" );
document.write( "both problems, the other solution was not the same as the\r\n" );
document.write( "other solution in the first problem. \r\n" );
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document.write( "Edwin \n" );
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