document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135991>Question 135991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have another question. My professor wants us to solve these equations in four different ways and show our work. I have been able to do the simpler equations but when they have 3 or 4 variables it gets a little bit more complicated.\r<BR>\n" );
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document.write( "I need to use the elimination method, substitution method, determinant and coordinates for example if if x=0 y=-5 etc...\r<BR>\n" );
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document.write( "Here are two problems that I'm having a hard time with.\r<BR>\n" );
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document.write( "#5<BR>\n" );
document.write( "x+y+z=6<BR>\n" );
document.write( "2x-y+3z=9<BR>\n" );
document.write( "-x+2y+z=6\r<BR>\n" );
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document.write( "#7<BR>\n" );
document.write( "3x+2y+z=6<BR>\n" );
document.write( "2x-y+4z=-4<BR>\n" );
document.write( "x+y-2z=5\r<BR>\n" );
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document.write( "Each one has to be done in four different ways. Thanks again for all the help.\r<BR>\n" );
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document.write( "Anne\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99660 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=99660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you say 'coordinate' method, do you mean to solve the system by graphing?  I certainly hope not because there is no way to render a three-dimensional coordinate system on this site.  However, I'll do one of your systems by the other three methods.\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=6 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y%2B3z=9 ALIGN=MIDDLE  ALT=\"2x-y%2B3z=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B2y%2Bz=6 ALIGN=MIDDLE  ALT=\"-x%2B2y%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Elimination:<BR>\n" );
document.write( "Replace Eq. 2 with the sum of Eq. 2 and two times Eq. 3.<BR>\n" );
document.write( "Replace Eq. 3 with the sum of Eq. 1 and Eq. 3.<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=6 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B3y%2B5z=21 ALIGN=MIDDLE  ALT=\"0x%2B3y%2B5z=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B3y%2B2z=12 ALIGN=MIDDLE  ALT=\"0x%2B3y%2B2z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Replace Eq. 3 with the sum of Eq. 2 and -1 times Eq. 3.<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=6 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B3y%2B5z=21 ALIGN=MIDDLE  ALT=\"0x%2B3y%2B5z=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y%2B3z=9 ALIGN=MIDDLE  ALT=\"0x%2B0y%2B3z=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide Eq 3 by 3<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=6 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B3y%2B5z=21 ALIGN=MIDDLE  ALT=\"0x%2B3y%2B5z=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y%2Bz=3 ALIGN=MIDDLE  ALT=\"0x%2B0y%2Bz=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Replace Eq. 1 with the sum of Eq. 1 and -1 times Eq. 3<BR>\n" );
document.write( "Replace Eq. 2 with the sum of Eq. 2 and -5 times Eq. 3<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2B0z=3 ALIGN=MIDDLE  ALT=\"x%2By%2B0z=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B3y%2B0z=6 ALIGN=MIDDLE  ALT=\"0x%2B3y%2B0z=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y%2Bz=3 ALIGN=MIDDLE  ALT=\"0x%2B0y%2Bz=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide Eq. 2 by 3<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2B0z=3 ALIGN=MIDDLE  ALT=\"x%2By%2B0z=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2By%2B0z=2 ALIGN=MIDDLE  ALT=\"0x%2By%2B0z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y%2Bz=3 ALIGN=MIDDLE  ALT=\"0x%2B0y%2Bz=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Replace Eq. 1 with the sum of Eq. 1 and -1 times Eq. 2<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B0y%2B0z=1 ALIGN=MIDDLE  ALT=\"x%2B0y%2B0z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2By%2B0z=2 ALIGN=MIDDLE  ALT=\"0x%2By%2B0z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y%2Bz=3 ALIGN=MIDDLE  ALT=\"0x%2B0y%2Bz=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the variables with zero coefficients<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=3 ALIGN=MIDDLE  ALT=\"z=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "========================================================<BR>\n" );
document.write( "Substitution:\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=6 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y%2B3z=9 ALIGN=MIDDLE  ALT=\"2x-y%2B3z=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B2y%2Bz=6 ALIGN=MIDDLE  ALT=\"-x%2B2y%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve Eq. 1 for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-y-z ALIGN=MIDDLE  ALT=\"x=6-y-z\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute the expression for x into the other two equations<BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%286-y-z%29-y%2B3z=9 ALIGN=MIDDLE  ALT=\"2%286-y-z%29-y%2B3z=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%286-y-z%29%2B2y%2Bz=6 ALIGN=MIDDLE  ALT=\"-%286-y-z%29%2B2y%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute and collect like terms:<BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-2y-2z-y%2B3z=9 ALIGN=MIDDLE  ALT=\"12-2y-2z-y%2B3z=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y%2Bz=-3 ALIGN=MIDDLE  ALT=\"-3y%2Bz=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (New Eq. 2)\r<BR>\n" );
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document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2By%2Bz%2B2y%2Bz=6 ALIGN=MIDDLE  ALT=\"-6%2By%2Bz%2B2y%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2B2z=12 ALIGN=MIDDLE  ALT=\"3y%2B2z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (New Eq. 3)\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Solve equation 2 for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y=-3-z ALIGN=MIDDLE  ALT=\"-3y=-3-z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2B%28z%2F3%29 ALIGN=MIDDLE  ALT=\"y=1%2B%28z%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute this expression for y into the new Eq. 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%2Bz%2F3%29%2B2z=12 ALIGN=MIDDLE  ALT=\"3%281%2Bz%2F3%29%2B2z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Distribute, simplify, collect terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B3z%2F3%2B2z=12 ALIGN=MIDDLE  ALT=\"3%2B3z%2F3%2B2z=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2B2z=12-3 ALIGN=MIDDLE  ALT=\"z%2B2z=12-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3z=9 ALIGN=MIDDLE  ALT=\"3z=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=3 ALIGN=MIDDLE  ALT=\"z=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute this value for z into the new Eq. 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y%2B3=-3 ALIGN=MIDDLE  ALT=\"-3y%2B3=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y=-6 ALIGN=MIDDLE  ALT=\"-3y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute the values for y and z into the original equation 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=6 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%2B3=6 ALIGN=MIDDLE  ALT=\"x%2B2%2B3=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "============================================================<BR>\n" );
document.write( "Cramer's Rule\r<BR>\n" );
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document.write( "Create and evaluate the coefficient determinant\r<BR>\n" );
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document.write( "D =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C1%2C1%2C1%2C2%2C-1%2C3%2C-1%2C2%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C1%2C1%2C1%2C2%2C-1%2C3%2C-1%2C2%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you don't remember how to evaluate a determinant, here is a little cartoon that shows the process.  You have to take your coefficient determinant and make a 5X3 matrix by repeating the 1st and 2nd columns first.  Then follow the process shown:\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%29b%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( "Yours evaluates to: -9, so we say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-9 ALIGN=MIDDLE  ALT=\"D=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, replace the first column representing the coefficients on the x terms with the constant term values.\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%2C1%2C1%2C9%2C-1%2C3%2C6%2C2%2C1%29%29 ALIGN=MIDDLE  ALT=\"D%5Bx%5D=%28matrix%283%2C3%2C6%2C1%2C1%2C9%2C-1%2C3%2C6%2C2%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and do the determinant evaluation on t<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;\" >\r<BR>\n" );
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document.write( "This works out to -9 as well, so you can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bx%5D=-9 ALIGN=MIDDLE  ALT=\"D%5Bx%5D=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Cramer's rule says:\r<BR>\n" );
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document.write( "<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;\" >.  In this case:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2F-9=1 ALIGN=MIDDLE  ALT=\"-9%2F-9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Just as I most sincerely hope you expected)\r<BR>\n" );
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document.write( "As you might suspect, you replace the second column with the coefficients to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5By%5D ALIGN=MIDDLE  ALT=\"D%5By%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the third column to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bz%5D ALIGN=MIDDLE  ALT=\"D%5Bz%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then <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;\" > and <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( "I'll give you the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5By%5D ALIGN=MIDDLE  ALT=\"D%5By%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bz%5D ALIGN=MIDDLE  ALT=\"D%5Bz%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > matrices and you can do the calculations for yourself.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5By%5D=%28matrix%283%2C3%2C1%2C6%2C1%2C2%2C9%2C3%2C-1%2C6%2C1%29%29 ALIGN=MIDDLE  ALT=\"D%5By%5D=%28matrix%283%2C3%2C1%2C6%2C1%2C2%2C9%2C3%2C-1%2C6%2C1%29%29\"   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=D%5Bz%5D=%28matrix%283%2C3%2C1%2C1%2C6%2C2%2C-1%2C9%2C-1%2C2%2C6%29%29 ALIGN=MIDDLE  ALT=\"D%5Bz%5D=%28matrix%283%2C3%2C1%2C1%2C6%2C2%2C-1%2C9%2C-1%2C2%2C6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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