document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140461>Question 1140461</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Use a matrix approach to solve the system. Express the solutions as 4-tuples of the form <BR>\n" );
document.write( "(x1, x2, x3, x4).<BR>\n" );
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document.write( "x1 − 3x2 − 2x3 + x4	 = 	−2<BR>\n" );
document.write( "−2x1 + 7x2 + x3 − 2x4	 = 	−3<BR>\n" );
document.write( "3x1 − 7x2 − 3x3 + 3x4	 = 	−2<BR>\n" );
document.write( "5x1 + x2 + 4x3 − 2x4	 = 	16<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760996 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=760996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+-+3x%5B2%5D+-+2x%5B3%5D+%2B+x4%09=+-2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+-+3x%5B2%5D+-+2x%5B3%5D+%2B+x4%09=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5B1%5D+%2B+7x%5B2%5D+%2B+x%5B3%5D+-+2x%5B4%5D%09=+-3 ALIGN=MIDDLE  ALT=\"-2x%5B1%5D+%2B+7x%5B2%5D+%2B+x%5B3%5D+-+2x%5B4%5D%09=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5B1%5D+-+7x%5B2%5D+-+3x%5B3%5D+%2B+3x%5B4%5D%09=+-2 ALIGN=MIDDLE  ALT=\"3x%5B1%5D+-+7x%5B2%5D+-+3x%5B3%5D+%2B+3x%5B4%5D%09=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5B1+%5D%2B+x%5B2+%5D%2B+4x%5B3%5D+-2x%5B4%5D%09=+16 ALIGN=MIDDLE  ALT=\"5x%5B1+%5D%2B+x%5B2+%5D%2B+4x%5B3%5D+-2x%5B4%5D%09=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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%284%2C5%2C%0D%0A1%2C-3%2C-2%2C1%2C-2%2C%0D%0A-2%2C7%2C1%2C-2%2C-3%2C%0D%0A3%2C-7%2C-3%2C3%2C-2%2C%0D%0A5%2C1%2C4%2C-2%2C16%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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%284%2C5%2C%0D%0A1%2C%09-3%2C%09-2%2C%091%2C%09-2%2C%0D%0A-2%2C%097%2C%091%2C%09-2%2C%09-3%2C%0D%0A3%2C%09-7%2C%09-3%2C%093%2C%09-2%2C%0D%0A5%2C%091%2C%094%2C%09-2%2C%0916%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Eliminate the 1st column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A%0D%0A1%2C%09-3%2C%09-2%2C%091%2C%09-2%2C%0D%0A0%2C%091%2C%09-3%2C%090%2C%09-7%2C%0D%0A0%2C%092%2C%093%2C%090%2C%094%2C%0D%0A0%2C%0916%2C%0914%2C%09-7%2C%0926%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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%284%2C5%2C%0D%0A%0D%0A1%2C%09-3%2C%09-2%2C%091%2C%09-2%2C%0D%0A0%2C%091%2C%09-3%2C%090%2C%09-7%2C%0D%0A0%2C%092%2C%093%2C%090%2C%094%2C%0D%0A0%2C%0916%2C%0914%2C%09-7%2C%0926%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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%284%2C5%2C%0D%0A%0D%0A1%2C%090%2C%09-11%2C%091%2C%09-23%2C%0D%0A0%2C%091%2C%09-3%2C%090%2C%09-7%2C%0D%0A0%2C%090%2C%099%2C%090%2C%0918%2C%0D%0A0%2C%090%2C%0962%2C%09-7%2C%09138%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Make the pivot in the 3rd column by dividing the 3rd row by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A%0D%0A1%2C%090%2C%09-11%2C%091%2C%09-23%2C%0D%0A0%2C%091%2C%09-3%2C%090%2C%09-7%2C%0D%0A0%2C%090%2C%091%2C%090%2C%092%2C%0D%0A0%2C%090%2C%0962%2C%09-7%2C%09138%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Eliminate the 3rd column\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A%0D%0A1%2C%090%2C%090%2C%091%2C%09-1%2C%0D%0A0%2C%091%2C%090%2C%090%2C%09-1%2C%0D%0A0%2C%090%2C%091%2C%090%2C%092%2C%0D%0A0%2C%090%2C%090%2C%09-7%2C%0914%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Make the pivot in the 4th column by dividing the 4th row by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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%284%2C5%2C%0D%0A%0D%0A1%2C%090%2C%090%2C%091%2C%09-1%2C%0D%0A0%2C%091%2C%090%2C%090%2C%09-1%2C%0D%0A0%2C%090%2C%091%2C%090%2C%092%2C%0D%0A0%2C%090%2C%090%2C%091%2C%09-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Eliminate the 4th column:\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A%0D%0A1%2C%090%2C%090%2C%090%2C%091%2C%0D%0A0%2C%091%2C%090%2C%090%2C%09-1%2C%0D%0A0%2C%090%2C%091%2C%090%2C%092%2C%0D%0A0%2C%090%2C%090%2C%091%2C%09-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+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%5B2+%5D=+-1 ALIGN=MIDDLE  ALT=\"x%5B2+%5D=+-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%5B3%5D+=+2 ALIGN=MIDDLE  ALT=\"x%5B3%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D+=+-2 ALIGN=MIDDLE  ALT=\"x%5B4%5D+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );