document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199356>Question 1199356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Lower Colorado River consists of a series of four reservoirs. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results:\r<BR>\n" );
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document.write( "* I don't know how to type in matrices here without looking messy, please Google search the above statements to obtain the equation :( *\r<BR>\n" );
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document.write( "a) Find normalized eigenvectors for Q, you may use MATLAB or any other software to find your answers. [5 marks]\r<BR>\n" );
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document.write( "I already calculated the above part, which the eigenvalues are basically just 11.797, 12.252, 12.377 and 13.422, but I couldn't solve the next question: \r<BR>\n" );
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document.write( "b) Hence, using your answer in (a), given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+K%5E4 ALIGN=MIDDLE  ALT=\"Q+=+K%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+det%28Q-lambda+I%29+=+0+ ALIGN=MIDDLE  ALT=\"+det%28Q-lambda+I%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (lambda is the eigenvalue), eigenvalue property of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%5En+=+P+%2A+D%5En+%2A+P%5E-1+ ALIGN=MIDDLE  ALT=\"+Q%5En+=+P+%2A+D%5En+%2A+P%5E-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+K+=+Q%5E4+%2A+v3+ ALIGN=MIDDLE  ALT=\"+K+=+Q%5E4+%2A+v3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, v3 is the eigenvector obtained from the third eigenvalue, 12.377. Calculate matrix K. [1 mark]\r<BR>\n" );
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document.write( "It only worth 1 mark, I think there's a faster way to solve it like by using Cayley-Hamilton Theorem, I'm not really sure, please help me<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 #833211 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "I found this link with a solution:\r<BR>\n" );
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document.write( "Problem 12.8<BR>\n" );
document.write( "The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P12.8. Mass balances can be written for each reservoir and the following set of simultaneous linear algebraic equations results:\r<BR>\n" );
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document.write( "https://webstersean.wordpress.com/problems-and-solutions-from-chapters-11-and-12/\r<BR>\n" );
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document.write( "I hope it will help. </SPAN>\n" );
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