document.write( "Question 1182942: Solve the given equation by Guass elimination method;\r
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\n" ); document.write( " 1x₂-1x₃+2x₄=3 \n" ); document.write( "
Algebra.Com's Answer #813108 by ikleyn(52781)\"\" \"About 
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document.write( "4x1 - 3x2 + x3 = -8\r\n" );
document.write( "-2x1 + x2 - 3x3 = -4\r\n" );
document.write( "x1 - x2 + 2x3 = 3\r\n" );
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document.write( "Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)\r\n" );
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document.write( "4	-3	1	-8\r\n" );
document.write( "-2	1	-3	-4\r\n" );
document.write( "1	-1	2	3\r\n" );
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document.write( "R1 / 4 → R1 (divide the 1 row by 4)\r\n" );
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document.write( "1	-0.75	0.25	-2\r\n" );
document.write( "-2	1	-3	-4\r\n" );
document.write( "1	-1	2	3\r\n" );
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document.write( "R2 + 2 R1 → R2 (multiply 1 row by 2 and add it to 2 row); R3 - 1 R1 → R3 (multiply 1 row by 1 and subtract it from 3 row)\r\n" );
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document.write( "1	-0.75	0.25	-2\r\n" );
document.write( "0	-0.5	-2.5	-8\r\n" );
document.write( "0	-0.25	1.75	5\r\n" );
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document.write( "R2 / -0.5 → R2 (divide the 2 row by -0.5)\r\n" );
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document.write( "1	-0.75	0.25	-2\r\n" );
document.write( "0	1	5	16\r\n" );
document.write( "0	-0.25	1.75	5\r\n" );
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document.write( "R1 + 0.75 R2 → R1 (multiply 2 row by 0.75 and add it to 1 row); R3 + 0.25 R2 → R3 (multiply 2 row by 0.25 and add it to 3 row)\r\n" );
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document.write( "1	0	4	10\r\n" );
document.write( "0	1	5	16\r\n" );
document.write( "0	0	3	9\r\n" );
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document.write( "R3 / 3 → R3 (divide the 3 row by 3)\r\n" );
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document.write( "1	0	4	10\r\n" );
document.write( "0	1	5	16\r\n" );
document.write( "0	0	1	3\r\n" );
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document.write( "R1 - 4 R3 → R1 (multiply 3 row by 4 and subtract it from 1 row); R2 - 5 R3 → R2 (multiply 3 row by 5 and subtract it from 2 row)\r\n" );
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document.write( "1	0	0	-2\r\n" );
document.write( "0	1	0	1\r\n" );
document.write( "0	0	1	3\r\n" );
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document.write( "x1 = -2\r\n" );
document.write( "x2 = 1\r\n" );
document.write( "x3 = 3\r\n" );
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document.write( "Make a check:\r\n" );
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document.write( "4·(-2) - 3·1 + 3 = -8 - 3 + 3 = -8\r\n" );
document.write( "-2·(-2) + 1 - 3·3 = 4 + 1 - 9 = -4\r\n" );
document.write( "(-2) - 1 + 2·3 = -2 - 1 + 6 = 3\r\n" );
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document.write( "ANSWER\r\n" );
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document.write( "x1 = -2\r\n" );
document.write( "x2 = 1\r\n" );
document.write( "x3 = 3\r\n" );
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