Mediante el método de Gauss, resuelve el sistema lineal: \( \begin{aligned} 2 x_{1}+3 x_{2}+2 x_{3} & =4 \\ x_{1}+4 x_{2}+x_{3} & =5 \\ 3 x_{1}+x_{2}+3 x_{3} & =7 \\ 4 x_{1}+5 x_{2}+4 x_{3} & =12 \\ 3 x_{1}+7 x_{2}+3 x_{3} & =9\end{aligned} \)

\( 1 \leftarrow \quad \) Determine whether \( B \) is the inverse of \( A \). \( A=\left[\begin{array}{rr}3 & -7 \\ -2 & 5\end{array}\right], \quad B=\left[\begin{array}{ll}5 & 7 \\ 2 & 3\end{array}\right] \)

\( \begin{array}{l}\text { Simplify the expression. Assume that variables represent } \\ \text { non-zero real numbers. }\end{array} \) \( \begin{array}{ll}\frac{6 a^{5}\left(a^{-2}\right)^{6}}{\left(a^{-1}\right)^{-3}} & \frac{6 a^{5}\left(a^{-2}\right)^{6}}{\left(a^{-1}\right)^{-3}}=\square \\ \text { (Simplify your answer. Type in exponenti. } \\ \text { notation. Type positive exponents.) }\end{array} \)

Rewrite the following without an exponent \[ (-7)^{-2} \]

\begin{tabular}{l|l}\( \begin{array}{l}\text { Simplify the expression so that no negative exponents } \\ \text { appear in the final result. Assume all variables represent } \\ \text { nonzero real numbers. }\end{array} \) & \( \begin{array}{l}\left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}=\square \\ \\ \left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}\end{array} \) \\ exponents only.) \end{tabular}

a) \( x+y=2 \) b) \( x+x-y=4+y \)