1. Diberikan \( G L_{2}(\mathbb{R})=\left\{\left.\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \right\rvert\, a, b, c, d \in \mathbb{R}, a d-b c \neq 0\right\} \) grup terhadap operasi perkalian matriks. Diberikan \( S L_{2}(\mathbb{R})=\left\{\left.\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \right\rvert\, a, b, c, d \in \mathbb{R}, a d-b c=1\right\} \). Buktikan bahwa \( S L_{2}(\mathbb{R}) \) subgrup dari \( G L_{2}(\mathbb{R}) \). 2. Diberikan \( M_{2}(\mathbb{R})=\left\{\left.\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \right\rvert\, a, b, c, d \in \mathbb{R}\right\} \) grup terhadap operasi penjumlahan matriks Buktikan bahwa \( N=\left\{\left.\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \right\rvert\, a, b, c, d \in \mathbb{R}, a+b=c+d\right\} \) subgrup dari \( M_{2}(\mathbb{R}) \).

Find \( x \). \( \frac{x-1}{3}=\frac{5}{x}+1 \) A. 6.36 OR -2.36 (B) 6.36 (C) 5.46 OR 2.36 (D) No real roots

3. At a school, \( 40 \% \) of the sikthegrade students said that hip-hop is their favorite kind of music. If 100 sixth-gade students preler hip hop music, how many sixth-grade studer are at the school? Explain or show your reasoning.

3.18. Determine el máximo comun divisor de los enteros \( 15,18,24 \) y escríbalo como una combinación lineal de \( 15,18,24 \). 3.19. Sea \( a \in \mathbb{Z}^{+} \)tal que \( \operatorname{mcd}(240, a)=1 \), probar que \( 240 \mid a^{4}-1 \).

Exercice N1 \( \begin{array}{lll}\text { Simplifier les expressions suivantes puis calculer leur valeur: } \\ \begin{array}{lll}\text { 1. } a=5^{1,7} \times 5^{1,3} & \text { 2. } b=\left(2^{-\frac{1}{5}}\right)^{6} & \text { 3. } c=4^{-0,7} \times \times \frac{1}{4^{0,3}}\end{array} & \text { 4. } d=\frac{6^{4,5} \times 6^{2,3}}{\left(6^{1,6}\right)^{3}}\end{array} \)

(Express \( \frac{6}{7 h}-\frac{3-4 g}{14 h} \) as a single fraction in its simplest form. Ungkapkan \( \frac{6}{7 h}-\frac{3-4 g}{14 h} \) sebagai pecahan tunggal dalam bentuk termudah.