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 \( \sqrt[3]{\left(-\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^{2}} \). \( \left(\begin{array}{cc}1 & i \sqrt{3})^{3}\end{array}\right. \)

Prove that for three sets \( \mathrm{A}, \mathrm{B} \) and C . \( (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \) \( (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \) Define Cartesian nroduct of two sets.

Describe classification of models by function.

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

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