กำหนดปัญหาโปรแกรมเชิงเส้นต่อไปนี้ Maximize \( P=5 x_{1}-3 x_{2}+x_{3} \) Subject to \( \begin{array}{r}2 x_{1}-4 x_{2}+x_{3} \leq-3 \\ x_{1}+3 x_{2} \geq 5 \\ 4 x_{1}-x_{3}=7 \\ x_{2}+x_{3} \leq 12 \\ x_{1}, x_{2}, x_{3} \geq 0\end{array} \) ข้อใดต่อไปนี้ ไม่ใช่ เงื่อนไขของ modified problem \( \begin{array}{l}\text { (a) } 2 x_{1}-4 x_{2}+x_{3}+S_{1}=-3 \\ \text { (c) } 4 x_{1}-x_{3}+a_{2}=7\end{array} \)

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

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.

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

4. If \( \quad\left[\begin{array}{cccccc}0 & 0 & -3 & -2 & 0 & 5 \\ -2 & 3 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -2 & 0 & 0 \\ 1 & -2 & 3 & 0 & 0 & 0 \\ -2 & 8 & 3 & 6 & 2 & 7 \\ 0 & 2 & 3 & 0 & 0 & 0\end{array}\right] \operatorname{compute} \operatorname{det}(A),(\operatorname{adj}(A))^{-1} \) and \( \operatorname{det}(\operatorname{adj}(A)) \)

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