Exorcise 3.11 . Let \( \mathrm{A}=\left(\begin{array}{ccc}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 6 & -5\end{array}\right) \). Find the matrix obtained from \( A \) by applying the following elementary row operation. \( \begin{array}{lll}\text { a. } R_{1} \leftrightarrow R_{3} & \text { b. } R_{2} \rightarrow R_{2}-4 R_{1} & \text { c. } R_{3} \rightarrow \frac{1}{3} R_{3}\end{array} \)

2. Вычислить и построить на комплексной плоскости число \( \sqrt[3]{\left(-\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^{2}} \). \( \left(\begin{array}{cc}1 & i \sqrt{3})^{3}\end{array}\right. \)

Which of the following is not correct? (a) Duality does not play any role in the post - opti mal analysis of on LPP. (b) The optimum simplex table provides informa tion about the status and worth of the resources in addition to the optimum values of the decision variables. (c) In the optimum solution of a profit maximization LPp, the total (optimum) profit must be equal to the total wortiof the resources. (d) To write the dual problem, it is necessary that its primal LPP must have all its variables as greater than or equal to zero.

Exorcise 3.11 . Let \( \mathrm{A}=\left(\begin{array}{ccc}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 6 & -5\end{array}\right) \). Find the matrix obtained from \( A \) by applying the following elementary row operation. \( \begin{array}{lll}\text { a. } R_{1} \leftrightarrow R_{3} & \text { b. } R_{2} \rightarrow R_{2}-4 R_{1} & \text { c. } R_{3} \rightarrow \frac{1}{3} R_{3}\end{array} \)

Describe classification of models by function.

1. Find the Eigen values of the matrix \( A=\left[\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & 2\end{array}\right] \)