document.write( "Question 1122545: solve the linear system by Gauss–Jordan
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\n" ); document.write( "− 2b + 3c = 1
\n" ); document.write( "3a + 6b − 3c = −2
\n" ); document.write( "6a + 6b + 3c = 5 \n" ); document.write( "
Algebra.Com's Answer #738699 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
.
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\n" ); document.write( "\n" ); document.write( "which, in particular, makes the Gauss-Jordan elimination.\r
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\n" ); document.write( "\n" ); document.write( "So, I inputted the augmented matrix and pressed the \"Solve\" button.\r
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\n" ); document.write( "\n" ); document.write( "The solver does not select a most efficient way, but, in any case, makes his work from the begginning to the very end.\r
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\n" ); document.write( "\n" ); document.write( "Below see the results:\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	0	-2	3	1\r\n" );
document.write( "2	3	6	-3	-2\r\n" );
document.write( "3	6	6	3	5\r\n" );
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document.write( "Make the pivot in the 1st column by dividing the 2nd row by 3 and swap the 2nd and the 1st rows\r\n" );
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document.write( "      X1	X2	X3	b\r\n" );
document.write( "1	1	2	-1	-2/3\r\n" );
document.write( "2	0	-2	3	1\r\n" );
document.write( "3	6	6	3	5\r\n" );
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document.write( "Multiply the 1st row by 6\r\n" );
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document.write( "      X1	X2	X3	b\r\n" );
document.write( "1	6	12	-6	-4\r\n" );
document.write( "2	0	-2	3	1\r\n" );
document.write( "3	6	6	3	5\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	-2/3\r\n" );
document.write( "2	0	-2	3	1\r\n" );
document.write( "3	0	-6	9	9\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	2	-1	-2/3\r\n" );
document.write( "2	0	1	-3/2	-1/2\r\n" );
document.write( "3	0	-6	9	9\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	-2/3\r\n" );
document.write( "2	0	2	-3	-1\r\n" );
document.write( "3	0	-6	9	9\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	2	1/3\r\n" );
document.write( "2	0	1	-3/2	-1/2\r\n" );
document.write( "3	0	-6	9	9\r\n" );
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document.write( "Multiply the 2nd row by -6\r\n" );
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document.write( "      X1	X2	X3	b\r\n" );
document.write( "1	1	0	2	1/3\r\n" );
document.write( "2	0	-6	9	3\r\n" );
document.write( "3	0	-6	9	9\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	1/3\r\n" );
document.write( "2	0	1	-3/2	-1/2\r\n" );
document.write( "3	0	0	0	6\r\n" );
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\n" ); document.write( "\n" ); document.write( "Do you see this last line of the transformed matrix which consists of zero coefficients with non-zero right side ?\r
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\n" ); document.write( "\n" ); document.write( "It means that the system is INCONSISTENT.\r
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