document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152209>Question 152209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the system using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination: \r<BR>\n" );
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document.write( "w+x+y+z=5<BR>\n" );
document.write( "w+2x-y-2z=-1<BR>\n" );
document.write( "w-3x-3y-z=-1<BR>\n" );
document.write( "2w-x+2y-z=-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111917 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=111917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1 1   1  1  5<BR>\n" );
document.write( "1 2  -1 -2 -1<BR>\n" );
document.write( "1 -3 -3 -1 -1<BR>\n" );
document.write( "2 -1  2 -1 -2\r<BR>\n" );
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document.write( "-R1+R2, -R1+R3<BR>\n" );
document.write( "1 1   1  1  5<BR>\n" );
document.write( "0 1  -2 -3 -6<BR>\n" );
document.write( "0 -4 -4 -2 -6<BR>\n" );
document.write( "2 -1  2 -1 -2\r<BR>\n" );
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document.write( "-2R1+R4<BR>\n" );
document.write( "1 1   1  1  5<BR>\n" );
document.write( "0 1  -2 -3 -6<BR>\n" );
document.write( "0 -4 -4 -2 -6<BR>\n" );
document.write( "0 -3  0 -3 -12\r<BR>\n" );
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document.write( "-1/3R4, -1/2R3<BR>\n" );
document.write( "1  1  1  1  5<BR>\n" );
document.write( "0  1 -2 -3 -6<BR>\n" );
document.write( "0  2  2  1  3<BR>\n" );
document.write( "0  1  0  1  4\r<BR>\n" );
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document.write( "-R2+R1, -R2+R4<BR>\n" );
document.write( "1  0  3  4  11<BR>\n" );
document.write( "0  1 -2 -3 -6<BR>\n" );
document.write( "0  2  2  1  3<BR>\n" );
document.write( "0  0  2  4  10\r<BR>\n" );
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document.write( "-2R2+R3<BR>\n" );
document.write( "1  0  3  4  11<BR>\n" );
document.write( "0  1 -2 -3 -6<BR>\n" );
document.write( "0  0  6  7  15<BR>\n" );
document.write( "0  0  2  4  10\r<BR>\n" );
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document.write( "1/2R4 <-> R3<BR>\n" );
document.write( "1  0  3  4  11<BR>\n" );
document.write( "0  1 -2 -3 -6<BR>\n" );
document.write( "0  0  1  2  5<BR>\n" );
document.write( "0  0  6  7  15\r<BR>\n" );
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document.write( "-3R3+R1,2R3+R2, -6R3+R4<BR>\n" );
document.write( "1  0  0 -2  -4<BR>\n" );
document.write( "0  1  0  1   4<BR>\n" );
document.write( "0  0  1  2   5<BR>\n" );
document.write( "0  0  0 -5  -3\r<BR>\n" );
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document.write( "-1/5R5<BR>\n" );
document.write( "1  0  0 -2  -4<BR>\n" );
document.write( "0  1  0  1   4<BR>\n" );
document.write( "0  0  1  2   5<BR>\n" );
document.write( "0  0  0  1  3/5\r<BR>\n" );
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document.write( "-2R4+R3,-R4+R2, 2R4+R1<BR>\n" );
document.write( "1  0  0  0 -14/5<BR>\n" );
document.write( "0  1  0  0  17/5<BR>\n" );
document.write( "0  0  1  0  19/5<BR>\n" );
document.write( "0  0  0  1  3/5\r<BR>\n" );
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document.write( "This gives solution set {-14/5, 17/5, 19/5, 3/5}. </SPAN>\n" );
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