document.write( "Question 1005940: (by matrices) 3x+2y=3
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Algebra.Com's Answer #622101 by AnlytcPhil(1807) $\"\"$ $\"About$
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document.write( "There are two ways to do this by matrices.  \r\n" );
document.write( "Augmented matrix (Gauss-Jordan) and inverse\r\n" );
document.write( "method.  I picked the 1st method:\r\n" );
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document.write( "We abbreviate that system with this augmented matrix:\r\n" );
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document.write( "We want 0's where the 2 and 5 are.\r\n" );
document.write( "and 1's where the 3 (upper left corner) \r\n" );
document.write( "and -4 are.\r\n" );
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document.write( "We'll get the 0's first.\r\n" );
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document.write( "To get a 0 where the 5 is,\r\n" );
document.write( "multiply row 1 by -5 and \r\n" );
document.write( "row 2 by 3 and replace row 2.\r\n" );
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document.write( "Here's the work:      -15 -10 | -15\r\n" );
document.write( "                       15 -12 |  81\r\n" );
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document.write( "                        0 -22 |  66\r\n" );
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document.write( "Since it turns out that that all those numbers\r\n" );
document.write( "can be divided through by -22, we will do that\r\n" );
document.write( "too, getting \r\n" );
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document.write( "                        0   1 |  -3 \r\n" );
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document.write( "and replace row 2 by that:\r\n" );
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document.write( "Then we get a 0 where the 2 is by multiplying the\r\n" );
document.write( "second row by -2 and adding it to the first row:\r\n" );
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document.write( "Here's the work:        3   2 |   3\r\n" );
document.write( "                        0  -2 |   6\r\n" );
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document.write( "                        3   0 |   9\r\n" );
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document.write( "Since it turns out that that all those numbers\r\n" );
document.write( "can be divided through by 3, we will do that\r\n" );
document.write( "too, getting \r\n" );
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document.write( "                        1   0 |   3\r\n" );
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document.write( "and replace row 1 by that:\r\n" );
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document.write( "This augmented matrix is the abbreviation for \r\n" );
document.write( "this system:\r\n" );
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document.write( "or x = 3\r\n" );
document.write( "   y = -3\r\n" );
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document.write( "Edwin
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