document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=985432>Question 985432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This was on a Hero's episode (Season 4, Episode 1) that never showed the solution, and thought I would place it up here as I came up with 2 answer myself, was wanting validation to my answer: (w=0,x=12/5,y=19/5,z=0) or (w=1, x=1, y=1, and z=1), the second set of answers I never actually worked out to be that, I just saw that answer automatically in my head, and it does indeed work, but I am unsure how to show the work for it, and would love someone to walk me through that if they wouldn't mind.\r<BR>\n" );
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document.write( "x + 2y + 3w + 4z = 10\r<BR>\n" );
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document.write( "2x - y + w - z = 1\r<BR>\n" );
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document.write( "3x + y + 4w + 3z = 11\r<BR>\n" );
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document.write( "-2x + 6y + 4w + 10z = 18<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 #606256 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=606256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The determinant of the 4x4 matrix of this system is equal to zero.\r<BR>\n" );
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document.write( "So, the matrix is singular, actually.\r<BR>\n" );
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document.write( "Therefore, it is not amazing that you found two solutions of the system. \r<BR>\n" );
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document.write( "Indeed, there are infinitely many solutions. \r<BR>\n" );
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document.write( "<U>The trick</U>: I did not calculate the determinant myself.\r<BR>\n" );
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document.write( "I simply asked GOOGLE, and it pointed me to this solver (online calculator):\r<BR>\n" );
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document.write( "http://ncalculators.com/matrix/4x4-matrix-determinant-calculator.htm \r<BR>\n" );
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document.write( "I don't know why, but I trust to this result. \r<BR>\n" );
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