document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443606>Question 443606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> need to find the determinate of the following:  please help!\r<BR>\n" );
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document.write( "3    0    -5    0<BR>\n" );
document.write( "-5   1     1    2<BR>\n" );
document.write( "2    7     1    0<BR>\n" );
document.write( "-1   0     1    0\r<BR>\n" );
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document.write( "thx! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305925 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have this matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C3%2C0%2C-5%2C0%2C-5%2C1%2C1%2C2%2C2%2C7%2C1%2C0%2C-1%2C0%2C1%2C0%29 ALIGN=MIDDLE  ALT=\"matrix%284%2C4%2C3%2C0%2C-5%2C0%2C-5%2C1%2C1%2C2%2C2%2C7%2C1%2C0%2C-1%2C0%2C1%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The only way to find the determinant is to use cofactor expansion.<BR>\n" );
document.write( "Find the row or column with the most 0s or easy to work with numbers. I'm going to choose row 4.\r<BR>\n" );
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document.write( "Start with A[41].\r<BR>\n" );
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document.write( "It has a -1.\r<BR>\n" );
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document.write( "Cross out all values in row 4, and in column 1 to get this matrix:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C0%2C-5%2C0%2C1%2C1%2C2%2C7%2C1%2C0%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C0%2C-5%2C0%2C1%2C1%2C2%2C7%2C1%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Now find its determinant:<BR>\n" );
document.write( "I assume you know how to find the determinant of a 3x3.<BR>\n" );
document.write( "[0 + -70 + 0] - [0 + 0 + 0] = -70\r<BR>\n" );
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document.write( "So we have -1*-70 * (-1)^(1+4) = 70 * -1 = -70\r<BR>\n" );
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document.write( "So for cell[41] our cofactor is -70.\r<BR>\n" );
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document.write( "A[42] is 0\r<BR>\n" );
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document.write( "A[43] is 1\r<BR>\n" );
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document.write( "A[44] is 0\r<BR>\n" );
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document.write( "So focus on cell[43]\r<BR>\n" );
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document.write( "Cross out all values in row 4 and col 3.\r<BR>\n" );
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document.write( "To get this 3x3 matrix: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C3%2C0%2C0%2C-5%2C1%2C2%2C2%2C7%2C0%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C3%2C0%2C0%2C-5%2C1%2C2%2C2%2C7%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Again, find it's determinant: -42\r<BR>\n" );
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document.write( "So we have 1 * -42 * (-1)^(4+3) = -42 * -1 = 42<BR>\n" );
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document.write( "To put it together take C41 + C43 to get -70 + 42 = -28<BR>\n" );
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document.write( "Our determinant of this 4x4 = -28\r<BR>\n" );
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document.write( " </SPAN>\n" );
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