document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20884>Question 20884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a matrix equation equivalent to the system of equations.<BR>\n" );
document.write( "9x + 9y = -9<BR>\n" );
document.write( "5x - 2y = 6\r<BR>\n" );
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document.write( "Cramer's rule.<BR>\n" );
document.write( "6x + 4y = -4<BR>\n" );
document.write( "y = -3x - 7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12176 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write a matrix equation equivalent to the system of equations.<BR>\n" );
document.write( "9x + 9y = -9<BR>\n" );
document.write( "5x - 2y = 6 <BR>\n" );
document.write( "we write the matrix equation as (A)*(X)=(C)..where A is the (2,2)matrix of coefficients namely,9,9,5 and -2 here.X is the (2,1) matrix of unknowns x and y and C is the constants (2,1)matrix on the right side of the eqn NAMELY -9 AND 6.you will find that from the rule for equality of matrices,the above matrix eqn.in effect means the same as that of the given equations.<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C2%2C9%2C9%2C5%2C-2%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C2%2C9%2C9%2C5%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)*(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2Cx%2Cy%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2Cx%2Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C-9%2C6%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C-9%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Cramer's rule.<BR>\n" );
document.write( "6x + 4y = -4<BR>\n" );
document.write( "y = -3x - 7<BR>\n" );
document.write( "GIVING BELOW EXAMPE OF CRAMERS RULE.<BR>\n" );
document.write( "My question is.... I was wondering how to do the cramer rule on a 3x3. I have found a bunch of examples and stuff, but I want to know how in the world do you find the determinants of the D, Dx, Dy.and Dz. If you could just tell me how, that would be great.<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 9496 by venugopalramana(585) About Me  on 2005-11-15 10:49:54 (Show Source):<BR>\n" );
document.write( "SEE THE FOLLOWING AND COME BACK IF YOU HAVE DIFFICULTY.HERE C,CX,CY,CZ REFER TO YOUR D,DX,DY,DZ...JUST A DIFFERENCE IN NOMENCLATURE.I SHOWED IN DETAIL A 2X2 DETERMINANT AND THEN IN BRIEF A 3X3 DETERMINANT<BR>\n" );
document.write( "2x+y=4<BR>\n" );
document.write( "3x-y=6<BR>\n" );
document.write( "make a deteminant with coefficients of x (2,3)and y(1,-1) in the 2 eqns.call it C.(Actually for a determinant as you know ,the numbers are contained in vertical bars at either end like |xx|,but in the following the bars are omitted due to difficulty in depiction.you may assume the bars are present)<BR>\n" );
document.write( "C=matrix(2,2,2,1,3,-1)=2*(-1)-(1*3)=-5<BR>\n" );
document.write( "..now use the constants (4,6)to replace coefficients of x(2,3) in the above determinant C...call it CX..<BR>\n" );
document.write( "CX=matrix(2,2,4,1,6,-1)=4*(-1)-1*6=-4-6=-10<BR>\n" );
document.write( "..now use the constants (4,6)to replace coefficients of y(1,-1) in the above determinant C...call it CY..<BR>\n" );
document.write( "CY=matrix(2,2,2,4,3,6)=2*6-3*4=12=12=0<BR>\n" );
document.write( "..now cramers rule says that<BR>\n" );
document.write( "(x/CX)=(y/CY)=(1/C)..so we get<BR>\n" );
document.write( "x/(-10)=y/0=1/-5<BR>\n" );
document.write( "x=-10/-5=10/5=2<BR>\n" );
document.write( "y=0/-5=0<BR>\n" );
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document.write( "so using the above method you can do the next problem ..here due to presence of 3 variables you will get 3rd.order determinants...4 in all...namely C,CX,CY and CZ,the last formula also extends to include z ,<BR>\n" );
document.write( "(x/CX)=(y/CY)=(z/CZ)=(1/C)..<BR>\n" );
document.write( "but the procedure is same ..<BR>\n" );
document.write( "2x+3y+ z= 5<BR>\n" );
document.write( "x+y-2z= -2<BR>\n" );
document.write( "-3x +z=-7 ...<BR>\n" );
document.write( "...just to give you the idea<BR>\n" );
document.write( "C=matrix(3,3,2,3,1,1,1,-2,-3,0,1)..and<BR>\n" );
document.write( "CZ=matrix(3,3,2,3,5,1,1,-2,-3,0,7)..etc..hope you can work out the rest\r<BR>\n" );
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document.write( " </SPAN>\n" );
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