document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159570>Question 1159570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system\r<BR>\n" );
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document.write( "5x1 - 6x2 + 3x3 + 4x4 = 4<BR>\n" );
document.write( "-x1 +  x2 + 3x3 + 2x4 = 5<BR>\n" );
document.write( "4x1 - 5x2 + 6x3 + 6x4 = 9<BR>\n" );
document.write( "-3x1+ 3x2 + 9x3 + 6x4 = 15<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782632 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=782632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
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%0A5%2C%09-6%2C%093%2C%094%2C%094%2C%0D%0A-1%2C%091%2C%093%2C%092%2C%095%2C%0D%0A4%2C%09-5%2C%096%2C%096%2C%099%2C%0D%0A-3%2C%093%2C%099%2C%096%2C%0915%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " its determinant  Δ = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the system of linear equations is either inconsistent or has infinitely many solutions. Gauss-Jordan elimination method will help get the complete answer.\r<BR>\n" );
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document.write( "Find the pivot in the 1st column (inversing the sign in the whole row) and swap the 2nd and the 1st rows\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%09-1%2C%09-3%2C%09-2%2C%09-5%2C%0D%0A5%2C%09-6%2C%093%2C%094%2C%094%2C%0D%0A4%2C%09-5%2C%096%2C%096%2C%099%2C%0D%0A-3%2C%093%2C%099%2C%096%2C%0915%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the 1st row by 5\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%0A5%2C%09-5%2C%09-15%2C%09-10%2C%09-25%2C%0D%0A5%2C%09-6%2C%093%2C%094%2C%094%2C%0D%0A4%2C%09-5%2C%096%2C%096%2C%099%2C%0D%0A-3%2C%093%2C%099%2C%096%2C%0915%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the 1st row from the 2nd row and restore it\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%09-1%2C%09-3%2C%09-2%2C%09-5%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A4%2C%09-5%2C%096%2C%096%2C%099%2C%0D%0A-3%2C%093%2C%099%2C%096%2C%0915%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the 1st row by 4\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%0A4%2C%09-4%2C%09-12%2C%09-8%2C%09-20%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A4%2C%09-5%2C%096%2C%096%2C%099%2C%0D%0A-3%2C%093%2C%099%2C%096%2C%0915%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the 1st row from the 3rd row and restore it\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%09-1%2C%09-3%2C%09-2%2C%09-5%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A-3%2C%093%2C%099%2C%096%2C%0915%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the 1st row by -3\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%0A-3%2C%093%2C%099%2C%096%2C%0915%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A-3%2C%093%2C%099%2C%096%2C%0915%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the 1st row from the 4th row and restore it\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%09-1%2C%09-3%2C%09-2%2C%09-5%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%090%2C%090%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 (inversing the sign in the whole 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%09-1%2C%09-3%2C%09-2%2C%09-5%2C%0D%0A0%2C%091%2C%09-18%2C%09-14%2C%09-29%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%090%2C%090%2C%090%2C%090%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the 2nd row by -1\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%09-1%2C%09-3%2C%09-2%2C%09-5%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%090%2C%090%2C%090%2C%090%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the 2nd row from 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%090%2C%09-21%2C%09-16%2C%09-34%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%09-1%2C%0918%2C%0914%2C%0929%2C%0D%0A0%2C%090%2C%090%2C%090%2C%090%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the 2nd row from the 3rd row and restore it\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%090%2C%09-21%2C%09-16%2C%09-34%2C%0D%0A0%2C%091%2C%09-18%2C%09-14%2C%09-29%2C%0D%0A0%2C%090%2C%090%2C%090%2C%090%2C%0D%0A0%2C%090%2C%090%2C%090%2C%090%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%5B1%5D+=+-34+%2B+21x%5B3%5D+%2B+16x%5B4%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-34+%2B+21x%5B3%5D+%2B+16x%5B4%5D\"   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+=+-29+%2B+18x%5B3%5D+%2B+14x%5B4%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+-29+%2B+18x%5B3%5D+%2B+14x%5B4%5D\"   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%5B3%5D ALIGN=MIDDLE  ALT=\"x%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D ALIGN=MIDDLE  ALT=\"x%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > - free\r<BR>\n" );
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document.write( " </SPAN>\n" );
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