document.write( "Question 1139653: Use the Gauss-Jordan elimination method to solve the system of linear Equations:
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Algebra.Com's Answer #760146 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here's one exactly like it.  Just put your numbers instead:\r\n" );
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document.write( "2x +  y -  z = 2 \r\n" );
document.write( " x +  y +  z = 2 \r\n" );
document.write( " x + 3y + 2z = 1\r\n" );
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document.write( "The object is to get the matrix like this:\r\n" );
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document.write( "where there will be 1's on the diagonal, 0's underneath the\r\n" );
document.write( "diagonal, and numbers where the @'s are.\r\n" );
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document.write( "Start with:\r\n" );
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document.write( "Swap rows 1 and 2, because it's easier when there's a 1\r\n" );
document.write( "in the upper left corner.\r\n" );
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document.write( "R1 <-> R2\r\n" );
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document.write( "Multiply row 1 by -2\r\n" );
document.write( "-2R1->R1\r\n" );
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document.write( "Add Row 1 and Row 2 and put that in place of Row 2\r\n" );
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document.write( "R1+R2->R2 \r\n" );
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document.write( "Restore Row 1 both \r\n" );
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document.write( "R1/(-2) -> R1\r\n" );
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document.write( "Multiply Row 1 by -1\r\n" );
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document.write( "Add row 1 to Row 3\r\n" );
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document.write( "Restore row 1\r\n" );
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document.write( "-R1 <-> R1\r\n" );
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document.write( "Multiply row 2 by -1\r\n" );
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document.write( "-R2 <-> R2\r\n" );
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document.write( "Multiply Row by -2\r\n" );
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document.write( "Add row 2 and Row 3 and put that sum in row 3\r\n" );
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document.write( "R2+R3 -> R3\r\n" );
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document.write( "Restore Row 2\r\n" );
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document.write( "R2/(-2) -> R2\r\n" );
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document.write( "Divide row 3 by -5\r\n" );
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document.write( "R3/(-5)( -> R3\r\n" );
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document.write( "Rewrite as a system of equations:\r\n" );
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document.write( "1x + 1y + 1z = 2\r\n" );
document.write( "0x + 1y + 3z = 2\r\n" );
document.write( "0x + 0y + 1z = 1\r\n" );
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document.write( "Remove the understood 1's and 0's\r\n" );
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document.write( "x + y +  z = 2\r\n" );
document.write( "    y + 3z = 2\r\n" );
document.write( "         z = 1\r\n" );
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document.write( "The bottom equation of the system is already solved for z\r\n" );
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document.write( "         z = 1\r\n" );
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document.write( "Substitute in the middle equation of the system for y:\r\n" );
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document.write( "    y + 3z =  2\r\n" );
document.write( "  y + 3(1) =  2\r\n" );
document.write( "     y + 3 =  2\r\n" );
document.write( "         y = -1\r\n" );
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document.write( " Substitute in the top equation of the system for z\r\n" );
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document.write( "    x + y +  z = 2\r\n" );
document.write( "x + (-1) + (1) = 2\r\n" );
document.write( "             x = 2  \r\n" );
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document.write( "(x,y,z) = (2,-1,1)\r\n" );
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document.write( "Edwin
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