document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094810>Question 1094810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the following system of equations are consistent, independent and inconsistent <BR>\n" );
document.write( "t-u+2v-3w=9<BR>\n" );
document.write( "4t+11v-10w=46<BR>\n" );
document.write( "3t-u+8v-6w=27. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709429 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52908)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=709429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Your matrix\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	1	-1	2	-3	9\r\n" );
document.write( "2	4	0	11	-10	46\r\n" );
document.write( "3	3	-1	8	-6	27\r\n" );
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document.write( "Find the pivot in the 1st column in the 1st row\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	1	-1	2	-3	9\r\n" );
document.write( "2	4	0	11	-10	46\r\n" );
document.write( "3	3	-1	8	-6	27\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	X4	b\r\n" );
document.write( "1	4	-4	8	-12	36\r\n" );
document.write( "2	4	0	11	-10	46\r\n" );
document.write( "3	3	-1	8	-6	27\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	X4	b\r\n" );
document.write( "1	1	-1	2	-3	9\r\n" );
document.write( "2	0	4	3	2	10\r\n" );
document.write( "3	3	-1	8	-6	27\r\n" );
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document.write( "Multiply the 1st row by 3\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	3	-3	6	-9	27\r\n" );
document.write( "2	0	4	3	2	10\r\n" );
document.write( "3	3	-1	8	-6	27\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	X4	b\r\n" );
document.write( "1	1	-1	2	-3	9\r\n" );
document.write( "2	0	4	3	2	10\r\n" );
document.write( "3	0	2	2	3	0\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	X4	b\r\n" );
document.write( "1	1	-1	2	-3	9\r\n" );
document.write( "2	0	1	3/4	1/2	5/2\r\n" );
document.write( "3	0	2	2	3	0\r\n" );
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document.write( "Multiply the 2nd row by -1\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	1	-1	2	-3	9\r\n" );
document.write( "2	0	-1	-3/4	-1/2	-5/2\r\n" );
document.write( "3	0	2	2	3	0\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	X4	b\r\n" );
document.write( "1	1	0	11/4	-5/2	23/2\r\n" );
document.write( "2	0	1	3/4	1/2	5/2\r\n" );
document.write( "3	0	2	2	3	0\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	X4	b\r\n" );
document.write( "1	1	0	11/4	-5/2	23/2\r\n" );
document.write( "2	0	2	3/2	1	5\r\n" );
document.write( "3	0	2	2	3	0\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	X4	b\r\n" );
document.write( "1	1	0	11/4	-5/2	23/2\r\n" );
document.write( "2	0	1	3/4	1/2	5/2\r\n" );
document.write( "3	0	0	1/2	2	-5\r\n" );
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document.write( "Make the pivot in the 3rd column by dividing the 3rd row by 1/2\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	1	0	11/4	-5/2	23/2\r\n" );
document.write( "2	0	1	3/4	1/2	5/2\r\n" );
document.write( "3	0	0	1	4	-10\r\n" );
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document.write( "Multiply the 3rd row by 11/4\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	1	0	11/4	-5/2	23/2\r\n" );
document.write( "2	0	1	3/4	1/2	5/2\r\n" );
document.write( "3	0	0	11/4	11	-55/2\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	X4	b\r\n" );
document.write( "1	1	0	0	-27/2	39\r\n" );
document.write( "2	0	1	3/4	1/2	5/2\r\n" );
document.write( "3	0	0	1	4	-10\r\n" );
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document.write( "Multiply the 3rd row by 3/4\r\n" );
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document.write( "        X1	X2	X3	X4	b\r\n" );
document.write( "1	1	0	0	-27/2	39\r\n" );
document.write( "2	0	1	3/4	1/2	5/2\r\n" );
document.write( "3	0	0	3/4	3	-15/2\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	X4	b\r\n" );
document.write( "1	1	0	0	-27/2	39\r\n" );
document.write( "2	0	1	0	-5/2	10\r\n" );
document.write( "3	0	0	1	4	-10\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = 39 + (27/2)x4\r\n" );
document.write( "x2 = 10 + (5/2)x4\r\n" );
document.write( "x3 = -10 - 4x4\r\n" );
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document.write( "x4 - free\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Consistent and independent.\r<BR>\n" );
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document.write( "About the term \"independent system of equations\" see this Wikipedia article\r<BR>\n" );
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document.write( "https://en.wikipedia.org/wiki/Independent_equation\r<BR>\n" );
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document.write( "About the term \"consistent/inconsistent system of equations\" see this Wikipedia article\r<BR>\n" );
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document.write( "https://en.wikipedia.org/wiki/Consistent_and_inconsistent_equations\r<BR>\n" );
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document.write( "Happy learning !\r<BR>\n" );
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document.write( " </SPAN>\n" );
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