Q. 15 Find the eigenvalues and eigenvectors of the matrix \( \left[\begin{array}{ll}6 & 5 \\ 3 & 4\end{array}\right] \).

1. Representar en un diagrama de Venn el conjunto \( [A-(A \cap B)]^{C} \). Considere a) \( A \) subconjunto de \( B \) b) \( B \) subconjunto de \( A \)

c) \( \begin{array}{l}\mathrm{U}=\{1,2,3, \ldots 10\} \text { is a given universal set. } O=\{1,3,5,7,9\} \text { and } \\ \mathrm{P}=\{\mathbf{3}, \mathbf{5}, 7\} \text { are any two given sets. } \\ \text { (i) Is the set } O \text { a subset of } U \text { ? Give reason. } \\ \text { (ii) Is the set } P \text { a proper or improper subset of } O \text { ? Give reason. } \\ \text { (iii) Show the sets } O \text { and } P \text { in a diagram. }\end{array} \).

Decision variables in an OR model are : (a) Controllable (b) Uncontrollable (c) Parameters (d) Constants

1-) \( \left(20\right. \) p) Let \( A=\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 3 & 4 \\ 5 & 2 & 0\end{array}\right] \) be a matrix. Find \( \operatorname{det}(A) \), adj \( A \) and the inverse of the matrix if it exists.

\( \mathrm{U}=\{1,2, \mathbf{3}, \ldots \mathbf{1 0}\} \) is a given universal set. \( \mathrm{O}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7} \), \( \mathrm{P}=\{\mathbf{3}, \mathbf{5}, 7\} \) are any two given sets. (i) Is the set \( O \) a subset of \( U \) ? Give reason.