document.write( "Question 1163482: Solve the following system of equations by Gauss elimination method :
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Algebra.Com's Answer #787577 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " x + 2y +  z = 2\r\n" );
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document.write( "3x +  y - 2z = 1 \r\n" );
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document.write( "4x - 3y -  z = 3\r\n" );
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document.write( "Your augmented matrix\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	2	1	2\r\n" );
document.write( "2	3	1	-2	1\r\n" );
document.write( "3	4	-3	-1	3\r\n" );
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document.write( "Find the pivot in the 1st column in the 1st row\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	2	1	2\r\n" );
document.write( "2	3	1	-2	1\r\n" );
document.write( "3	4	-3	-1	3\r\n" );
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document.write( "Multiply the 1st row by 3\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	3	6	3	6\r\n" );
document.write( "2	3	1	-2	1\r\n" );
document.write( "3	4	-3	-1	3\r\n" );
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document.write( "Subtract the 1st row from the 2nd row and restore it\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	2	1	2\r\n" );
document.write( "2	0	-5	-5	-5\r\n" );
document.write( "3	4	-3	-1	3\r\n" );
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document.write( "	Multiply the 1st row by 4\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	4	8	4	8\r\n" );
document.write( "2	0	-5	-5	-5\r\n" );
document.write( "3	4	-3	-1	3\r\n" );
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document.write( "Subtract the 1st row from the 3rd row and restore it\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	2	1	2\r\n" );
document.write( "2	0	-5	-5	-5\r\n" );
document.write( "3	0	-11	-5	-5\r\n" );
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document.write( "Make the pivot in the 2nd column by dividing the 2nd row by -5\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	2	1	2\r\n" );
document.write( "2	0	1	1	1\r\n" );
document.write( "3	0	-11	-5	-5\r\n" );
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document.write( "Multiply the 2nd row by 2\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	2	1	2\r\n" );
document.write( "2	0	2	2	2\r\n" );
document.write( "3	0	-11	-5	-5\r\n" );
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document.write( "Subtract the 2nd row from the 1st row and restore it\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	-1	0\r\n" );
document.write( "2	0	1	1	1\r\n" );
document.write( "3	0	-11	-5	-5\r\n" );
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document.write( "Multiply the 2nd row by -11\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	-1	0\r\n" );
document.write( "2	0	-11	-11	-11\r\n" );
document.write( "3	0	-11	-5	-5\r\n" );
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document.write( "Subtract the 2nd row from the 3rd row and restore it\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	-1	0\r\n" );
document.write( "2	0	1	1	1\r\n" );
document.write( "3	0	0	6	6\r\n" );
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document.write( "Make the pivot in the 3rd column by dividing the 3rd row by 6\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	-1	0\r\n" );
document.write( "2	0	1	1	1\r\n" );
document.write( "3	0	0	1	1\r\n" );
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document.write( "Multiply the 3rd row by -1\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	-1	0\r\n" );
document.write( "2	0	1	1	1\r\n" );
document.write( "3	0	0	-1	-1\r\n" );
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document.write( "Subtract the 3rd row from the 1st row\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	0	1\r\n" );
document.write( "2	0	1	1	1\r\n" );
document.write( "3	0	0	-1	-1\r\n" );
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document.write( "Multiply the 3rd row by -1\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	0	1\r\n" );
document.write( "2	0	1	1	1\r\n" );
document.write( "3	0	0	1	1\r\n" );
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document.write( "Subtract the 3rd row from the 2nd row and restore it\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	0	1\r\n" );
document.write( "2	0	1	0	0\r\n" );
document.write( "3	0	0	1	1\r\n" );
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document.write( "ANSWER.  The solution is (x,y,z) = (1,0,1).\r\n" );
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