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Solutiona) For node A,x_{1}+x_{2}=200For node B,x_{1}=x_{4}+x_{3}For node E.x_{2}+x_{3}=x_{5}For node D.x_{4}+x_{5}=200ar.\begin{array}{l}x_{1}+x_{2}=200 \\x_{1}-x_{3}-x_{4}=0 \\x_{2}+x_{3}-x_{5}=0 \\x_{4}+x_{5}=200\end{array}In matrix form, it c an be written or.\left[\begin{array}{ccccc}1 & 1 & 0 & 0 & 0 \\1 & 0 & -1 & -1 & 0 \\0 & 1 & 1 & 0 & -1 \\0 & 0 & 0 & 1 & 1\end{array}\right]\left[\begin{array}{c}x_{1} \\x_{2} \\x_{3} \\x_{4} \\x_{5}\end{array}\right]=\left[\begin{array}{cc}2 & 0 \\0 \\0 \\200\end{array}\right]b) Apply R_{1} \rightarrow R_{1}+R_{3}+2 R_{4}\begin{array}{c}{\left[\begin{array}{ccccc}1 & 2 & 1 & 2 & 1 \\1 & 0 & -1 & -1 & 0 \\0 & 1 & 1 & 0 & -1 \\0 & 0 & 0 & 1 & 1\end{array}\right]\left[\begin{array}{l}x_{1} \\x_{2} \\x_{3} \\x_{4} \\x_{5}\end{array}\right]=\left[\begin{array}{c}600 \\0 \\0 \\200\end{array}\right]} \\x_{1}+2 x_{2}+x_{3}+2 x_{4}+x_{5}=600 \\k\left(x_{1}+2 x_{2}+x_{3}+2 x_{4}+x_{5}\right)=600 k \\\text { Total time }=600 k\end{array}CSScanned with Carnscanner ...