document.write( "Question 1059848: Solve the system of linear equations using Gauss-Jordon elimination with back- substitution. Please show all work!\r
\n" ); document.write( "\n" ); document.write( "5x+7y+4z=23
\n" ); document.write( "4x+3y+8z=-6
\n" ); document.write( "5x+6y+5z=17\r
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Algebra.Com's Answer #674939 by ikleyn(52786)\"\" \"About 
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\n" ); document.write( "Solve the system of linear equations using Gauss-\"highlight%28cross%28Jordon%29%29\" Jordan elimination with back- substitution. Please show all work!\r
\n" ); document.write( "\n" ); document.write( "5x + 7y + 4z = 23
\n" ); document.write( "4x + 3y + 8z = -6
\n" ); document.write( "5x + 6y + 5z = 17
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document.write( "Solution set:\r\n" );
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document.write( "x1 = 5\r\n" );
document.write( "x2 = 2\r\n" );
document.write( "x3 = -4\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	5	7	4	23\r\n" );
document.write( "2	4	3	8	-6\r\n" );
document.write( "3	5	6	5	17\r\n" );
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document.write( "Make the pivot in the 1st column by dividing the 1st row by 5\r\n" );
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document.write( "№	X1	X2	X3	b\r\n" );
document.write( "1	1	7/5	4/5	23/5\r\n" );
document.write( "2	4	3	8	-6\r\n" );
document.write( "3	5	6	5	17\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	28/5	16/5	92/5\r\n" );
document.write( "2	4	3	8	-6\r\n" );
document.write( "3	5	6	5	17\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	7/5	4/5	23/5\r\n" );
document.write( "2	0	-13/5	24/5	-122/5\r\n" );
document.write( "3	5	6	5	17\r\n" );
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document.write( "Multiply the 1st row by 5\r\n" );
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document.write( "№	X1	X2	X3	b\r\n" );
document.write( "1	5	7	4	23\r\n" );
document.write( "2	0	-13/5	24/5	-122/5\r\n" );
document.write( "3	5	6	5	17\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	7/5	4/5	23/5\r\n" );
document.write( "2	0	-13/5	24/5	-122/5\r\n" );
document.write( "3	0	-1	1	-6\r\n" );
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document.write( "Find the pivot in the 2nd column (inversing the sign in the whole row) and swap the 3rd and the 2nd rows\r\n" );
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document.write( "№	X1	X2	X3	b\r\n" );
document.write( "1	1	7/5	4/5	23/5\r\n" );
document.write( "2	0	1	-1	6\r\n" );
document.write( "3	0	-13/5	24/5	-122/5\r\n" );
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document.write( "Multiply the 2nd row by 7/5\r\n" );
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document.write( "№	X1	X2	X3	b\r\n" );
document.write( "1	1	7/5	4/5	23/5\r\n" );
document.write( "2	0	7/5	-7/5	42/5\r\n" );
document.write( "3	0	-13/5	24/5	-122/5\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	11/5	-19/5\r\n" );
document.write( "2	0	1	-1	6\r\n" );
document.write( "3	0	-13/5	24/5	-122/5\r\n" );
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document.write( "Multiply the 2nd row by -13/5\r\n" );
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document.write( "№	X1	X2	X3	b\r\n" );
document.write( "1	1	0	11/5	-19/5\r\n" );
document.write( "2	0	-13/5	13/5	-78/5\r\n" );
document.write( "3	0	-13/5	24/5	-122/5\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	11/5	-19/5\r\n" );
document.write( "2	0	1	-1	6\r\n" );
document.write( "3	0	0	11/5	-44/5\r\n" );
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document.write( "Make the pivot in the 3rd column by dividing the 3rd row by 11/5\r\n" );
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document.write( "№	X1	X2	X3	b\r\n" );
document.write( "1	1	0	11/5	-19/5\r\n" );
document.write( "2	0	1	-1	6\r\n" );
document.write( "3	0	0	1	-4\r\n" );
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document.write( "Multiply the 3rd row by 11/5\r\n" );
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document.write( "№	X1	X2	X3	b\r\n" );
document.write( "1	1	0	11/5	-19/5\r\n" );
document.write( "2	0	1	-1	6\r\n" );
document.write( "3	0	0	11/5	-44/5\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	5\r\n" );
document.write( "2	0	1	-1	6\r\n" );
document.write( "3	0	0	1	-4\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	5\r\n" );
document.write( "2	0	1	-1	6\r\n" );
document.write( "3	0	0	-1	4\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	5\r\n" );
document.write( "2	0	1	0	2\r\n" );
document.write( "3	0	0	1	-4\r\n" );
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