document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131187>Question 1131187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> [1 2 -1 | 5]<BR>\n" );
document.write( "[0 1 -2 | 1]<BR>\n" );
document.write( "[0 1  0 | 0]<BR>\n" );
document.write( "Answer(3-3z, 1+2z, z)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "[1 2  1 | -3  ]<BR>\n" );
document.write( "[0 1 -3 | -1/2]<BR>\n" );
document.write( "[0 0  0 | 4   ]<BR>\n" );
document.write( "Answer(No Solutions)\r<BR>\n" );
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document.write( "I know the answers but I would like to know how to get them as well.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747806 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "First write down the augmented matrix and begin Gauss-Jordan elimination:\r<BR>\n" );
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document.write( "Your matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C+2%2C+-1%2C+5%2C0+%2C1%2C+-2+%2C+1%2C0+%2C1%2C+0+%2C+0%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C1%2C+2%2C+-1%2C+5%2C0+%2C1%2C+-2+%2C+1%2C0+%2C1%2C+0+%2C+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 1st column in the 1st row:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C%092%2C%09-1%2C%095%2C%0D%0A0%2C%091%2C%09-2%2C%091%2C%0D%0A0%2C%091%2C%090%2C%090%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 2nd column in the 2nd row:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C%092%2C%09-1%2C%095%2C%0D%0A0%2C%091%2C%09-2%2C%091%2C%0D%0A0%2C%091%2C%090%2C%090%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 2nd column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%090%2C%093%2C%093%2C%0D%0A0%2C%091%2C%09-2%2C%091%2C%0D%0A0%2C%090%2C%092%2C%09-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Make the pivot in the 3rd column by dividing the 3rd row by 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C%090%2C%093%2C%093%2C%0D%0A0%2C%091%2C%09-2%2C%091%2C%0D%0A0%2C%090%2C%091%2C%09-1%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 3rd column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C%090%2C%090%2C%099%2F2%2C%0D%0A0%2C%091%2C%090%2C%090%2C%0D%0A0%2C%090%2C%091%2C%09-1%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solution set:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9%2F2 ALIGN=MIDDLE  ALT=\"x+=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-1%2F2 ALIGN=MIDDLE  ALT=\"z+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check your answer: Answer(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-3z ALIGN=MIDDLE  ALT=\"3-3z\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2B2z ALIGN=MIDDLE  ALT=\"+1%2B2z\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3-3z=3-3%28-1%2F2%29=3%2B3%2F2=6%2F2%2B3%2F2=9%2F2 ALIGN=MIDDLE  ALT=\"x=3-3z=3-3%28-1%2F2%29=3%2B3%2F2=6%2F2%2B3%2F2=9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2B2z=1%2B2%28-1%2F2%29=1-1=0 ALIGN=MIDDLE  ALT=\"y=1%2B2z=1%2B2%28-1%2F2%29=1-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-3z ALIGN=MIDDLE  ALT=\"3-3z\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2B2z ALIGN=MIDDLE  ALT=\"+1%2B2z\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "Your matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C+2%2C+1%2C-3%2C0+%2C1%2C+-3+%2C+-1%2F2%2C0+%2C0%2C+0+%2C+4%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C1%2C+2%2C+1%2C-3%2C0+%2C1%2C+-3+%2C+-1%2F2%2C0+%2C0%2C+0+%2C+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 1st column in the 1st row:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C%092%2C%091%2C%09-3%2C%0D%0A0%2C%091%2C%09-3%2C%09-1%2F2%2C%0D%0A0%2C%090%2C%090%2C%094%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 2nd column in the 2nd row:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C1%2C%092%2C%091%2C%09-3%2C%0D%0A0%2C%091%2C%09-3%2C%09-1%2F2%2C%0D%0A0%2C%090%2C%090%2C%094%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 2nd column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%090%2C%097%2C%09-2%2C%0D%0A0%2C%091%2C%09-3%2C%09-1%2F2%2C%0D%0A0%2C%090%2C%090%2C%094%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solution set:\r<BR>\n" );
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document.write( "The system is inconsistent\r<BR>\n" );
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document.write( "The system of equations corresponding to this REF has as its third equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Ax+%2B+0%2Ay+%2B+0%2Az+=4 ALIGN=MIDDLE  ALT=\"0%2Ax+%2B+0%2Ay+%2B+0%2Az+=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This equation clearly has no solutions - no assignment of numerical values to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z ALIGN=MIDDLE  ALT=\"+z\"   DISABLED_style= \"max-width:90%; height:auto;\" > will make the value of the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Ax+%2B+0%2Ay+%2B+0%2Az ALIGN=MIDDLE  ALT=\"0%2Ax+%2B+0%2Ay+%2B+0%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to anything but zero. Hence the system has no solutions.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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