document.write( "Question 1194923: Please help me solve this Linear Equation using Matrices:\r
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\n" ); document.write( "4x1 − 8x2 + 4x3 = 48
\n" ); document.write( " 4x2 + 8x3 = 16
\n" ); document.write( "1.5x1 + x2 − 2.5x3 = −2\r
\n" ); document.write( "\n" ); document.write( "(x1, x2, x3) = \r
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Algebra.Com's Answer #827260 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Please help me solve this Linear Equation using Matrices:\r
\n" ); document.write( "\n" ); document.write( "Solve the following system of equations by reducing the augmented matrix.\r
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document.write( "4x1	 − 	8x2	 + 	4x3	 = 	48\r\n" );
document.write( "                4x2	 + 	8x3	 = 	16\r\n" );
document.write( "1.5x1	 + 	x2	 − 	2.5x3	 = 	−2\r\n" );
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document.write( "(x1, x2, x3) = \r\n" );
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\n" ); document.write( "\n" ); document.write( "                         S o l u t i o n\r
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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	4	-8	4	48\r\n" );
document.write( "2	0	4	8	16\r\n" );
document.write( "3	1.5	1	-2.5	-2\r\n" );
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document.write( "Make the pivot in the 1st column by dividing the 1st row by 4\r\n" );
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document.write( "        X1	X2	X3	b\r\n" );
document.write( "1	1	-2	1	12\r\n" );
document.write( "2	0	4	8	16\r\n" );
document.write( "3	1.5	1	-2.5	-2\r\n" );
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document.write( "Multiply the 1st row by 1.5\r\n" );
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document.write( "        X1	X2	X3	b\r\n" );
document.write( "1	1.5	-3	1.5	18\r\n" );
document.write( "2	0	4	8	16\r\n" );
document.write( "3	1.5	1	-2.5	-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	-2	1	12\r\n" );
document.write( "2	0	4	8	16\r\n" );
document.write( "3	0	4	-4	-20\r\n" );
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document.write( "Make the pivot in the 2nd column by dividing the 2nd row by 4\r\n" );
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document.write( "        X1	X2	X3	b\r\n" );
document.write( "1	1	-2	1	12\r\n" );
document.write( "2	0	1	2	4\r\n" );
document.write( "3	0	4	-4	-20\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	12\r\n" );
document.write( "2	0	-2	-4	-8\r\n" );
document.write( "3	0	4	-4	-20\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	5	20\r\n" );
document.write( "2	0	1	2	4\r\n" );
document.write( "3	0	4	-4	-20\r\n" );
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document.write( "Multiply the 2nd row by 4\r\n" );
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document.write( "        X1	X2	X3	b\r\n" );
document.write( "1	1	0	5	20\r\n" );
document.write( "2	0	4	8	16\r\n" );
document.write( "3	0	4	-4	-20\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	5	20\r\n" );
document.write( "2	0	1	2	4\r\n" );
document.write( "3	0	0	-12	-36\r\n" );
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document.write( "Make the pivot in the 3rd column by dividing the 3rd row by -12\r\n" );
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document.write( "        X1	X2	X3	b\r\n" );
document.write( "1	1	0	5	20\r\n" );
document.write( "2	0	1	2	4\r\n" );
document.write( "3	0	0	1	3\r\n" );
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document.write( "Multiply the 3rd row by 5\r\n" );
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document.write( "        X1	X2	X3	b\r\n" );
document.write( "1	1	0	5	20\r\n" );
document.write( "2	0	1	2	4\r\n" );
document.write( "3	0	0	5	15\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	2	4\r\n" );
document.write( "3	0	0	1	3\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	0	5\r\n" );
document.write( "2	0	1	2	4\r\n" );
document.write( "3	0	0	2	6\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	3\r\n" );
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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 = 3\r\n" );
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