document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198436>Question 1198436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the determinant for matrix [2 -1 -3, 1, 0 2, -1 2 1]\r<BR>\n" );
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document.write( "One of the following is the correct answer.  Which one?\r<BR>\n" );
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document.write( "A) 5<BR>\n" );
document.write( "B) 17<BR>\n" );
document.write( "C) 18<BR>\n" );
document.write( "D) -14<BR>\n" );
document.write( "E) -11<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 #832054 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Original matrix determinant<BR>\n" );
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document.write( "Copy the first two columns to place it to the right of the vertical bar like so<BR>\n" );
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document.write( "Then highlight these diagonals in red<BR>\n" );
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document.write( "Multiply everything in each diagonal separately<BR>\n" );
document.write( "A = 1st diagonal = 2*0*1 = 0<BR>\n" );
document.write( "B = 2nd diagonal = -1*2*(-1) = 2<BR>\n" );
document.write( "C = 3rd diagonal = -3*1*2 = -6<BR>\n" );
document.write( "Afterward you would add up the products<BR>\n" );
document.write( "D = A+B+C = 0+2+(-6) = -4<BR>\n" );
document.write( "We'll use this value later.\r<BR>\n" );
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document.write( "Repeat the same idea for these diagonals highlighted in blue.<BR>\n" );
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document.write( "Multiply everything in each diagonal separately<BR>\n" );
document.write( "E = 1st diagonal = -1*0*(-3) = 0<BR>\n" );
document.write( "F = 2nd diagonal = 2*2*2 = 8<BR>\n" );
document.write( "G = 3rd diagonal = 1*1*(-1) = -1<BR>\n" );
document.write( "Then add up the products<BR>\n" );
document.write( "H = E+F+G = 0 + 8 + (-1) = 7\r<BR>\n" );
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document.write( "The last step is to subtract the results of D and H to arrive at the determinant value.\r<BR>\n" );
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document.write( "Determinant of 3x3 matrix = D - H = -4 - 7 = <font color=red>-11</font>\r<BR>\n" );
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document.write( "Side note: the entire process shown above applies to 3x3 matrices only.\r<BR>\n" );
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document.write( "As an alternate method to compute the determinant, you can use a cofactor expansion.\r<BR>\n" );
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document.write( "You can use a tool like WolframAlpha or GeoGebra (both of which are free) to verify the answer.<BR>\n" );
document.write( "There are many other free online matrix determinant calculators out there.\r<BR>\n" );
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document.write( "-------------------------------------\r<BR>\n" );
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document.write( "Answer: <font color=red>-11  (choice E)</font><BR>\n" );
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