document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25255>Question 25255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When using gaussian elimination, can an inconsistant solution have a general solution? i worked out the matrix and came to a spot where 1=-3 and 1=10.4 (inconsistant 1 can't equal 2 different solutions); would there still be a way to formulate a general solution such as x=(2-4x,2-3x,x,0) = (2,2,0,0) + x(-4,-3,1,0)\r<BR>\n" );
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document.write( "I hope this is enough information to clearly explain my question. thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13546 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When using gaussian elimination, can an inconsistant solution have a general solution? i worked out the matrix and came to a spot where 1=-3 and 1=10.4 (inconsistant 1 can't equal 2 different solutions); would there still be a way to formulate a general solution such as x=(2-4x,2-3x,x,0) = (2,2,0,0) + x(-4,-3,1,0)<BR>\n" );
document.write( "I hope this is enough information to clearly explain my question. thanks<BR>\n" );
document.write( "I THINK YOU ARE CONFUSED BETWEEN ...INCONSISTENT,AND DEPENDENT EQUATIONS.<BR>\n" );
document.write( "AS THE NAME IMPLIES AN INCONSISTENT SET OF EQUATIONS HAS NO SOLUTION AS THEY ARE INCONSISTENT.FOR EXAMPLE <BR>\n" );
document.write( "X+Y=2<BR>\n" );
document.write( "2X+2Y=3....HENCE THERE IS NO QUESTION OF GETTING A GENERAL SOLUTION FOR THAT BY ANY METHOD GAUSSIAN ELIMINATION OR ANY..<BR>\n" );
document.write( "CONSISTENT AND DEPENDENT EQNS.HAVE INFINITE SOLUTIONS GIVEN BY A GENERAL FORMULA AS YOU HAVE MENTIONED..FOR EX.<BR>\n" );
document.write( "X+Y=1<BR>\n" );
document.write( "2X+2Y=2....THE GERAL FORMULA IS Y=1-X...OR (X,1-X)IS A SOLUTION SET..LIKE (1,0),(2,-1) ETC....<BR>\n" );
document.write( "FINALLY CONSISTENT AND INDEPENDENT EQNS.HAVE UNIQUE SOLUTION..FOR EXAMPLE<BR>\n" );
document.write( "X+Y=2<BR>\n" );
document.write( "X-Y=0...HAVE ONE UNIQUE SOLUTION X=1 AND Y=1<BR>\n" );
document.write( "NOW YOU CAN USE GAUSSIAN ELIMINATION TO THE 3 EXAMPLES ABOVE AND SEE WHAT YOU GET.IF YOU STILL AVE DIFFICULTY COME BACK </SPAN>\n" );
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