Answer:
(i) The given information can be written in the matrix form as \[\left[ \begin{matrix} 5 & 4 & 3 \\ 4 & 3 & 5 \\ 1 & 1 & 1 \\ \end{matrix} \right]\,\,\left[ \begin{matrix} x \\ y \\ z \\ \end{matrix} \right]=\left[ \begin{matrix} 11000 \\ 10700 \\ 2700 \\ \end{matrix} \right]\] Now, the linear equations are \[5x+4y+3z=11000\] \[4x+3y+5z=10700\] and \[x+y+z=2700\] (ii) Let \[A=\left[ \begin{matrix} 5 & 4 & 3 \\ 4 & 3 & 5 \\ 1 & 1 & 1 \\ \end{matrix} \right]\] Then, \[|A|=\left| \begin{matrix} 5 & 4 & 3 \\ 4 & 3 & 5 \\ 1 & 1 & 1 \\ \end{matrix} \right|\] \[=5\,(3-5)-4\,(4-5)+3\,(4-3)\] \[=-10+4+3=-\,3\ne 0\] \[\Rightarrow \] \[{{A}^{-1}}\] exists, so the equation have a unique solution. Hence, it is possible to solve the system of equations by using matrices. (iii) In my view, obedience should be rewarded most, because at school level, first of all students should be obedient to his/her teachers, then only he/she can liked by everyone.
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