document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=664130>Question 664130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Gauss-Jordan method to solve the system of equations.<BR>\n" );
document.write( "x-y=2<BR>\n" );
document.write( "y-z=0<BR>\n" );
document.write( "x+z=6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What is the solution set? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413135 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=413135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The system\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x-y=2<BR>\n" );
document.write( "y-z=0<BR>\n" );
document.write( "x+z=6 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "is the same as\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1x-1y+0z=2<BR>\n" );
document.write( "0x+1y-1z=0<BR>\n" );
document.write( "1x+0y+1z=6 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and that converts to this matrix\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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( "1	-1	0	2\r\n" );
document.write( "0	1	-1	0\r\n" );
document.write( "1	0	1	6\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now perform row reduction \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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( "1	-1	0	2\r\n" );
document.write( "0	1	-1	0\r\n" );
document.write( "1	0	1	6\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1	-1	0	2	\r\n" );
document.write( "0	1	-1	0	\r\n" );
document.write( "0	1	1	4	R3 + (-1)*R1\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1	0	-1	2	R1 + (1)*R2\r\n" );
document.write( "0	1	-1	0	\r\n" );
document.write( "0	1	1	4	\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1	0	-1	2	\r\n" );
document.write( "0	1	-1	0	\r\n" );
document.write( "0	0	2	4	R3 + (-1)*R2\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1	0	-1	2	\r\n" );
document.write( "0	1	-1	0	\r\n" );
document.write( "0	0	1	2	0.5*R3\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1	0	0	4	R1 + (1)*R3\r\n" );
document.write( "0	1	-1	0	\r\n" );
document.write( "0	0	1	2	\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1	0	0	4	\r\n" );
document.write( "0	1	0	2	R2 + (1)*R3\r\n" );
document.write( "0	0	1	2	\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The right hand column has the values, 4, 2 and 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So x = 4, y = 2, and z = 2 are the three solutions\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The solution as an ordered triple is therefore (4, 2, 2) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );