document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134302>Question 1134302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system using an augmented matrix in the reduced row echelon form. Be sure to<BR>\n" );
document.write( "show all elementary row operations. \r<BR>\n" );
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document.write( "x+y+z=-1<BR>\n" );
document.write( "x-y+5z=1<BR>\n" );
document.write( "2x+y+z=-4\r<BR>\n" );
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document.write( "I submitted this earlier but accidentally put z instead of the 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751703 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=751703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=-1 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%2B5z=1 ALIGN=MIDDLE  ALT=\"x-y%2B5z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%2Bz=-4 ALIGN=MIDDLE  ALT=\"2x%2By%2Bz=-4\"   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=matrix%283%2C4%2C1%2C1%2C1%2C-1%2C1%2C-1%2C5%2C1%2C2%2C1%2C1%2C-4%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C1%2C1%2C1%2C-1%2C1%2C-1%2C5%2C1%2C2%2C1%2C1%2C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Make zeros in column <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > except the entry at row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, column <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (pivot entry).\r<BR>\n" );
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document.write( "Subtract row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > from row<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   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=matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C-2%2C4%2C2%2C%0D%0A2%2C1%2C1%2C-4%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C-2%2C4%2C2%2C%0D%0A2%2C1%2C1%2C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Subtract row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C-2%2C4%2C2%2C%0D%0A0%2C-1%2C-1%2C-2%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C-2%2C4%2C2%2C%0D%0A0%2C-1%2C-1%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Make zeros in column <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > except the entry at row<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, column <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+ ALIGN=MIDDLE  ALT=\"2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >(pivot entry).\r<BR>\n" );
document.write( "\n" );
document.write( "Divide row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   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=matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C-1%2C-1%2C-2%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C-1%2C-1%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Subtract row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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=matrix%283%2C4%2C%0D%0A1%2C0%2C3%2C0%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C-1%2C-1%2C-2%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C0%2C3%2C0%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C-1%2C-1%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Add row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C0%2C3%2C0%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C-3%2C-3%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C0%2C3%2C0%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C-3%2C-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Make zeros in column <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > except the entry at row<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3 ALIGN=MIDDLE  ALT=\"+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, column<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3 ALIGN=MIDDLE  ALT=\"+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(pivot entry).\r<BR>\n" );
document.write( "\n" );
document.write( "Add row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C-3%2C-3%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C-3%2C-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Divide row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C1%2C1%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C1%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Add row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C0%2C1%2C%0D%0A0%2C0%2C1%2C1%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C0%2C1%2C%0D%0A0%2C0%2C1%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:  the reduced row echelon form is<BR>\n" );
document.write( "A[ref]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C0%2C1%2C%0D%0A0%2C0%2C1%2C1%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C0%2C1%2C%0D%0A0%2C0%2C1%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );