document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136905>Question 136905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried every solution and I cannot come up with an answer to this problem.<BR>\n" );
document.write( "I am trying to solve the problem by Crammer's Rule using determinants. The problem is: 3x - 2y+ z = 6<BR>\n" );
document.write( "            4x -4y + 3z = 0<BR>\n" );
document.write( "            5x - 4y + z = -5\r<BR>\n" );
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document.write( "I would very much appreciate your help,I have spent hours trying to find solutions to this problem.               Thank-you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100198 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=100198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1: Create the coefficient determinant and the answer column matrix\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=%28matrix%283%2C3%2C3%2C-2%2C1%2C4%2C-4%2C3%2C5%2C-4%2C1%29%29 ALIGN=MIDDLE  ALT=\"D=%28matrix%283%2C3%2C3%2C-2%2C1%2C4%2C-4%2C3%2C5%2C-4%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=%28matrix%283%2C1%2C6%2C0%2C-5%29%29 ALIGN=MIDDLE  ALT=\"AC=%28matrix%283%2C1%2C6%2C0%2C-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2: Evaluate the determinant.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%28%0D%0A%28matrix%283%2C5%2Cred%28a%29%2Cb%2Cc%2Ca%2Cb%2Cd%2Cred%28e%29%2Cf%2Cd%2Ce%2Cg%2Ch%2Cred%28i%29%2Cg%2Ch%29%29=red%28aei%29%2C%0D%0A%28matrix%283%2C5%2Ca%2Cred%28b%29%2Cc%2Ca%2Cb%2Cd%2Ce%2Cred%28f%29%2Cd%2Ce%2Cg%2Ch%2Ci%2Cred%28g%29%2Ch%29%29=aei%2Bred%28bfg%29%2C%0D%0A%28matrix%283%2C5%2Ca%2Cb%2Cred%28c%29%2Ca%2Cb%2Cd%2Ce%2Cf%2Cred%28d%29%2Ce%2Cg%2Ch%2Ci%2Cg%2Cred%28h%29%29%29=aei%2Bbfg%2Bred%28cdh%29%2C%28matrix%283%2C5%2Ca%2Cb%2Cred%28c%29%2Ca%2Cb%2Cd%2Cred%28e%29%2Cf%2Cd%2Ce%2Cred%28g%29%2Ch%2Ci%2Cg%2Ch%29%29=aei%2Bbfg%2Bcdh-%28red%28gec%29%29%2C%0D%0A%28matrix%283%2C5%2Ca%2Cb%2Cc%2Cred%28a%29%2Cb%2Cd%2Ce%2Cred%28f%29%2Cd%2Ce%2Cg%2Cred%28h%29%2Ci%2Cg%2Ch%29%29=aei%2Bbfg%2Bcdh-%28gec%2Bred%28hfa%29%29%2C%0D%0A%28matrix%283%2C5%2Ca%2Cb%2Cc%2Ca%2Cred%28b%29%2Cd%2Ce%2Cf%2Cred%28d%29%2Ce%2Cg%2Ch%2Cred%28i%29%2Cg%2Ch%29%29=aei%2Bbfg%2Bcdh-%28gec%2Bhfa%2Bred%28idb%29%29%29 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=green%28D%29=aei%2Bbfg%2Bcdh-gec-hfa-idb=red%28%283%2A-4%2A1%29%2B%28-2%2A3%2A5%29%2B%281%2A4%2A-4%29-%285%2A-4%2A1%29-%28-4%2A3%2A3%29-%281%2A4%2A-2%29%29=-12-30-16%2B20%2B36%2B8=green%286%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3: Now, take the coefficient determinant and replace the x-column (the first column) with the answer column, like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bx%5D=%28matrix%283%2C3%2C6%2C-2%2C1%2C0%2C-4%2C3%2C-5%2C-4%2C1%29%29 ALIGN=MIDDLE  ALT=\"D%5Bx%5D=%28matrix%283%2C3%2C6%2C-2%2C1%2C0%2C-4%2C3%2C-5%2C-4%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4: Evaluate the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bx%5D ALIGN=MIDDLE  ALT=\"D%5Bx%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > determinant as shown in step 2.\r<BR>\n" );
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document.write( "Cramer's rule states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=D%5Bx%5D%2FD ALIGN=MIDDLE  ALT=\"x=D%5Bx%5D%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5: Repeat step 3 and 4, except replace the y-column (the second column) with the answer column matrix and apply Cramer's rule: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=D%5By%5D%2FD ALIGN=MIDDLE  ALT=\"y=D%5By%5D%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6: Do it one more time replacing the z-column (the third column) with the answer column.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=D%5Bz%5D%2FD ALIGN=MIDDLE  ALT=\"z=D%5Bz%5D%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hint: Be extremely meticulous about the signs on the numbers when evaluating the determinants.  If you have access to Microsoft Excel, you can put the coefficients into a square set of cells, one coefficient per cell.  Let's say you put them in cells A1 through C3, then in an empty cell, type in =MDETERM(A1:C3).  When you hit enter, the value of the determinant will appear. </SPAN>\n" );
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