document.write( "Question 1105522: x+2y+3z+4w=0
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Algebra.Com's Answer #720365 by ikleyn(52908)\"\" \"About 
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document.write( "Your matrix\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	1	2	3	4	0\r\n" );
document.write( "2	8	5	1	4	0\r\n" );
document.write( "3	5	6	8	1	0\r\n" );
document.write( "4	8	3	7	2	0\r\n" );
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document.write( "Write down the main matrix and find its determinant\r\n" );
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document.write( "        X1	X2	X3	X4\r\n" );
document.write( "1	1	2	3	4\r\n" );
document.write( "2	8	5	1	4\r\n" );
document.write( "3	5	6	8	1\r\n" );
document.write( "4	8	3	7	2\r\n" );
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document.write( "Δ = -1034    <<<---=== Since the determinant is not zero, the solution to the system is the zero vector.\r\n" );
document.write( "                       Explicit calculations below confirm this fact.\r\n" );
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document.write( "Replace the 1st column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "        X1	X2	X3	X4\r\n" );
document.write( "1	0	2	3	4\r\n" );
document.write( "2	0	5	1	4\r\n" );
document.write( "3	0	6	8	1\r\n" );
document.write( "4	0	3	7	2\r\n" );
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document.write( "Δ1 = 0\r\n" );
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document.write( "Replace the 2nd column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "        X1	X2	X3	X4\r\n" );
document.write( "1	1	0	3	4\r\n" );
document.write( "2	8	0	1	4\r\n" );
document.write( "3	5	0	8	1\r\n" );
document.write( "4	8	0	7	2\r\n" );
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document.write( "Δ2 = 0\r\n" );
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document.write( "Replace the 3rd column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "        X1	X2	X3	X4\r\n" );
document.write( "1	1	2	0	4\r\n" );
document.write( "2	8	5	0	4\r\n" );
document.write( "3	5	6	0	1\r\n" );
document.write( "4	8	3	0	2\r\n" );
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document.write( "Δ3 = 0\r\n" );
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document.write( "Replace the 4th column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "        X1	X2	X3	X4\r\n" );
document.write( "1	1	2	3	0\r\n" );
document.write( "2	8	5	1	0\r\n" );
document.write( "3	5	6	8	0\r\n" );
document.write( "4	8	3	7	0\r\n" );
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document.write( "Δ4 = 0\r\n" );
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document.write( "x1 = Δ1 / Δ = 0 / (-1034) = 0\r\n" );
document.write( "x2 = Δ2 / Δ = 0 / (-1034) = 0\r\n" );
document.write( "x3 = Δ3 / Δ = 0 / (-1034) = 0\r\n" );
document.write( "x4 = Δ4 / Δ = 0 / (-1034) = 0\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = 0\r\n" );
document.write( "x2 = 0\r\n" );
document.write( "x3 = 0\r\n" );
document.write( "x4 = 0\r\n" );
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