document.write( "Question 1131309: Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
\n" ); document.write( "x + y + z = -5
\n" ); document.write( "x - y + 3z = -1
\n" ); document.write( "4x + y + z = -2
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Algebra.Com's Answer #747992 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Answer.  x = 1       \r\n" );
document.write( "         y = -4     \r\n" );
document.write( "         z = -2     \r\n" );
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document.write( "Your matrix\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	1	1	-5\r\n" );
document.write( "2	1	-1	3	-1\r\n" );
document.write( "3	4	1	1	-2\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	1	1	-5\r\n" );
document.write( "2	1	-1	3	-1\r\n" );
document.write( "3	4	1	1	-2\r\n" );
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document.write( "Subtract the 1st row from the 2nd row\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	1	1	-5\r\n" );
document.write( "2	0	-2	2	4\r\n" );
document.write( "3	4	1	1	-2\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	4	4	-20\r\n" );
document.write( "2	0	-2	2	4\r\n" );
document.write( "3	4	1	1	-2\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	1	1	-5\r\n" );
document.write( "2	0	-2	2	4\r\n" );
document.write( "3	0	-3	-3	18\r\n" );
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document.write( "Make the pivot in the 2nd column by dividing the 2nd row by -2\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	1	1	-5\r\n" );
document.write( "2	0	1	-1	-2\r\n" );
document.write( "3	0	-3	-3	18\r\n" );
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document.write( "Subtract the 2nd row from the 1st row\r\n" );
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document.write( "X1	X2	X3	b\r\n" );
document.write( "1	1	0	2	-3\r\n" );
document.write( "2	0	1	-1	-2\r\n" );
document.write( "3	0	-3	-3	18\r\n" );
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document.write( "Multiply the 2nd row by -3\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	2	-3\r\n" );
document.write( "2	0	-3	3	6\r\n" );
document.write( "3	0	-3	-3	18\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	2	-3\r\n" );
document.write( "2	0	1	-1	-2\r\n" );
document.write( "3	0	0	-6	12\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	2	-3\r\n" );
document.write( "2	0	1	-1	-2\r\n" );
document.write( "3	0	0	1	-2\r\n" );
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document.write( "Multiply the 3rd row by 2\r\n" );
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document.write( "	X1	X2	X3	b\r\n" );
document.write( "1	1	0	2	-3\r\n" );
document.write( "2	0	1	-1	-2\r\n" );
document.write( "3	0	0	2	-4\r\n" );
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document.write( "Subtract the 3rd 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	0	1\r\n" );
document.write( "2	0	1	-1	-2\r\n" );
document.write( "3	0	0	1	-2\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	-2\r\n" );
document.write( "3	0	0	-1	2\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	-4\r\n" );
document.write( "3	0	0	1	-2\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = 1      \r\n" );
document.write( "x2 = -4   \r\n" );
document.write( "x3 = -2   \r\n" );
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