document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044650>Question 1044650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what  condition  a &b must satisfy  so that the following system has nontrival<BR>\n" );
document.write( "solution?<BR>\n" );
document.write( "x+y+ax=0<BR>\n" );
document.write( "x+y+bz=0<BR>\n" );
document.write( "ax+by+z=0<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 #660011 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I will assume that your first equation is actually x+y+az = 0.\r<BR>\n" );
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document.write( "Simply equate the determinant of the coefficient matrix to 0:\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2C1%2C1%2Ca%2C1%2C1%2Cb%2Ca%2Cb%2C1%29%29+=+1%2Bab%2Bab-%28a%5E2%2Bb%5E2%2B1%29+=+0 ALIGN=MIDDLE   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=-a%5E2+%2B2ab+-+b%5E2+=+-%28a%5E2-2ab%2Bb%5E2%29+=+-%28a-b%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"-a%5E2+%2B2ab+-+b%5E2+=+-%28a%5E2-2ab%2Bb%5E2%29+=+-%28a-b%29%5E2+=+0\"   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=a+=+b ALIGN=MIDDLE  ALT=\"a+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for the system to have a non-trivial solution. </SPAN>\n" );
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