document.write( "Question 431371: help me solve using Gauss-Jordan elimination
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Algebra.Com's Answer #299396 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "2xl+4x2-10x3=-2\r\n" );
document.write( "3xl+9x2-2lx3=0\r\n" );
document.write( "1xl+5x2-12x3=1\r\n" );
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document.write( "The idea is to end up with a matrix that looks like this:\r\n" );
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document.write( "where there are numbers where the \"%22%23%22\"'s are\r\n" );
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document.write( "Divide row 1 by 2 to get a 1 in the upper left corner\r\n" );
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document.write( "Get a 0 under it by multiplying row 1 by -3\r\n" );
document.write( "and adding it to row 2 \"+matrix%282%2C5%2C%0D%0A-3%2C-6%2C15%2C%22%7C%22%2C3%2C%0D%0A3%2C9%2C-2l%2C%22%7C%22%2C0%29+\" getting \"+matrix%281%2C5%2C%0D%0A0%2C3%2C-6%2C%22%7C%22%2C3%29+\"\r\n" );
document.write( "Then replace row 2 by that\r\n" );
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document.write( "Get a 0 in the lower left by multiplying row 1 by -1\r\n" );
document.write( "and adding it to row 3 \"+matrix%282%2C5%2C%0D%0A-1%2C-2%2C5%2C%22%7C%22%2C1%2C%0D%0A1%2C5%2C-l2%2C%22%7C%22%2C1%29+\" getting \"+matrix%281%2C5%2C%0D%0A0%2C3%2C-7%2C%22%7C%22%2C2%29+\"\r\n" );
document.write( "Then replace row 3 by that\r\n" );
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document.write( "Get a 1 where the first 3 on the second row is by\r\n" );
document.write( "dividing the second row through by 3\r\n" );
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document.write( "Get a 0 where the 3 is on the bottom row\r\n" );
document.write( " by multiplying row 2 by -3\r\n" );
document.write( "and adding it to row 3 \"+matrix%282%2C5%2C%0D%0A0%2C-3%2C6%2C%22%7C%22%2C-3%2C%0D%0A0%2C3%2C-7%2C%22%7C%22%2C2%29+\" getting \"+matrix%281%2C5%2C%0D%0A0%2C0%2C-1%2C%22%7C%22%2C-1%29+\"\r\n" );
document.write( "Then replace row 3 by that\r\n" );
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document.write( "Now divide the bottom row through by -1 to\r\n" );
document.write( "get a 1, and you have the final matrix:\r\n" );
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document.write( "That means:\r\n" );
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document.write( "1x1 + 2x2 - 5x3 = -1\r\n" );
document.write( "0x1 + 1x2 - 2x3 =  1\r\n" );
document.write( "0x1 + 0x2 + 1x3 =  1\r\n" );
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document.write( "or simplifying,\r\n" );
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document.write( "x1 + 2x2 - 5x3 = -1\r\n" );
document.write( "x2 - 2x3 = 1\r\n" );
document.write( "x3 = 1\r\n" );
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document.write( "Substitute 1 for x3 in the middle equation:\r\n" );
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document.write( " x2 - 2x3 = 1\r\n" );
document.write( "x2 - 2(1) = 1\r\n" );
document.write( "   x2 - 2 = 1\r\n" );
document.write( "       x2 = 3\r\n" );
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document.write( "Substitute 1 for x3 and 3 for x1 in the top equation:\r\n" );
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document.write( "   x1 + 2x2 - 5x3 = -1\r\n" );
document.write( "x1 + 2(3) - 5(1) = -1\r\n" );
document.write( "      x1 + 6 - 5 = -1\r\n" );
document.write( "          x1 + 1 = -1\r\n" );
document.write( "              x1 = -2\r\n" );
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document.write( "Solution:  (x1,x2,x3) = (-2,3,1)\r\n" );
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document.write( "Edwin
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