document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442543>Question 442543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on a project, where I have to solve a matrix ( [2 5] [3 1] with the 2 being over the 3) by using cramer's rule. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305272 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=305272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given a matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C2%2C2%2C5%2C3%2C1%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C2%2C2%2C5%2C3%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cramer's rule states that the xi = det(Ai)/det(A)\r<BR>\n" );
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document.write( "So what is the det(A)?  det(A) = 2*1 - 3*5 = -13\r<BR>\n" );
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document.write( "You do not specify the solution matrix in this problem, but I will act like you did and you can apply it to your problem.\r<BR>\n" );
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document.write( "Let's say the solution matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C1%2C2%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C1%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then to solve for x1 you would create a matrix where the solution matrix is substituted in for column 1.\r<BR>\n" );
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document.write( "In this made up example, you'd find the det(A1) where A1 is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C2%2C1%2C5%2C2%2C1%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C2%2C1%2C5%2C2%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This determinant is 1 -10 = -9.\r<BR>\n" );
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document.write( "So the solution to x1 = -9/-13 = (9/13)\r<BR>\n" );
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document.write( "To find x2 create an A2 matrix.  \r<BR>\n" );
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document.write( "The matrix would be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C2%2C2%2C1%2C3%2C2%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C2%2C2%2C1%2C3%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The det(A2) = 4 - 3 = 1\r<BR>\n" );
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document.write( "So then x2 = 1 / -13 =  (-1/13)\r<BR>\n" );
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document.write( "To show that Cramer's rule indeed works:\r<BR>\n" );
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document.write( "2x1 + 5x2 = 1<BR>\n" );
document.write( "3x1 + 1x2 = 2\r<BR>\n" );
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document.write( "Where as I said <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C2%2C1%2C2%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C2%2C1%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is my solution matrix and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C2%2C2%2C5%2C3%2C1%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C2%2C2%2C5%2C3%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > was the matrix you gave me.\r<BR>\n" );
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document.write( "If I plug in x1=9/13 and x2=-1/13\r<BR>\n" );
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document.write( "2(9/13) + 5(-1/13) = 13/13 = 1.  Check.<BR>\n" );
document.write( "3(9/13) + 1(-1/13) = 26/13 = 2.  Check.\r<BR>\n" );
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document.write( "Now for whatever your solution matrix is, apply the same steps.<BR>\n" );
document.write( " </SPAN>\n" );
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