document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154259>Question 154259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help evaluate the determinate? Please explain everything so I can comprehend this...please.\r<BR>\n" );
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document.write( "|1 -3 2 0|<BR>\n" );
document.write( "|-3 -1 0 -2|<BR>\n" );
document.write( "|2 1 3 1|<BR>\n" );
document.write( "|2 0 -2 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113556 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=113556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> |1 -3 2 0|<BR>\n" );
document.write( "|-3 -1 0 -2|<BR>\n" );
document.write( "|2 1 3 1|<BR>\n" );
document.write( "|2 0 -2 0<BR>\n" );
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document.write( "Break it up into 4 3rd order matrices by eliminating one column at a time, and multiplying by the coefficient in the top row.  Also, the sign alternates, + and minus.\r<BR>\n" );
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document.write( "1 times\r<BR>\n" );
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document.write( "|-1  0 -2|<BR>\n" );
document.write( "| 1  3  1|<BR>\n" );
document.write( "| 0 -2  0|\r<BR>\n" );
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document.write( "= 1 times {-1  -2}<BR>\n" );
document.write( "= -1*2 -2<BR>\n" );
document.write( "= -2 + 4<BR>\n" );
document.write( "= 2<BR>\n" );
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document.write( "The 2nd sub matrix is negative<BR>\n" );
document.write( " - (-3) times<BR>\n" );
document.write( "|-3  0 -2|<BR>\n" );
document.write( "| 2  3  1|<BR>\n" );
document.write( "| 2 -2  0|\r<BR>\n" );
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document.write( "= 3 times [-3*(3*0 - (-2)*1)] -2<BR>\n" );
document.write( "= 3<BR>\n" );
document.write( "= 3<BR>\n" );
document.write( "= 42<BR>\n" );
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document.write( "The 3rd one is positive<BR>\n" );
document.write( "2 times<BR>\n" );
document.write( "|-3 -1 -2|<BR>\n" );
document.write( "| 2  1  1|<BR>\n" );
document.write( "| 2  0  0|\r<BR>\n" );
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document.write( "= 2 times [-3*(0) +1*(0 - 2) -2*(0 - 2)]<BR>\n" );
document.write( "= 2<BR>\n" );
document.write( "= 4<BR>\n" );
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document.write( "The 4th is zero.<BR>\n" );
document.write( "The Determinant is the sum, 2+42+4 = 48.<BR>\n" );
document.write( "It's an error prone calculation, which is why I made an Excel sheet that always gets it right. </SPAN>\n" );
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