document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107130>Question 107130</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0028242270/algebrahomeworkh>Algebra 2 with trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> solve using augmented matrices\r<BR>\n" );
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document.write( "6r+s=9<BR>\n" );
document.write( "3r+2s=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78091 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=78091\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the system\r<BR>\n" );
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document.write( "6r+s=9<BR>\n" );
document.write( "3r+2s=0\r<BR>\n" );
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document.write( "Now form an augmented matrix\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C6%2C1%2C9%2C3%2C2%2C0%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C6%2C1%2C9%2C3%2C2%2C0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply Row 1 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make the pivot 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C1%2F6%2C3%2F2%2C3%2C2%2C0%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C1%2F6%2C3%2F2%2C3%2C2%2C0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Add  -3*Row 1 to Row 2 to get the new Row 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C1%2F6%2C3%2F2%2C0%2C3%2F2%2C-9%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C1%2F6%2C3%2F2%2C0%2C3%2F2%2C-9%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply Row 2 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make the pivot 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C1%2F6%2C3%2F2%2C0%2C1%2C-3%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C1%2F6%2C3%2F2%2C0%2C1%2C-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Add  -1/6*Row 2 to Row 1 to get the new Row 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C0%2C2%2C0%2C1%2C-3%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C0%2C2%2C0%2C1%2C-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The matrix is now in <font size=4><b>reduced row echelon form</b></font>\r<BR>\n" );
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document.write( "So the answer is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-3 ALIGN=MIDDLE  ALT=\"s=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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