91Ó°ÊÓ

For the following exercises, solve each system by Gaussian elimination. $$ \begin{array}{c} x+y+z=14 \\ 2 y+3 z=-14 \\ -16 y-24 z=-112 \end{array} $$

For the following exercises, use the matrices below to perform matrix multiplication. \(A=\left[\begin{array}{rr}-1 & 5 \\ 3 & 2\end{array}\right], B=\left[\begin{array}{rrr}3 & 6 & 4 \\ -8 & 0 & 12\end{array}\right], C=\left[\begin{array}{rr}4 & 10 \\ -2 & 6 \\ 5 & 9\end{array}\right], D=\left[\begin{array}{rrr}2 & -3 & 12 \\ 9 & 3 & 1 \\ 0 & 8 & -10\end{array}\right]\) \(C B\)

For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. $$ \frac{-24 x-27}{(4 x+5)^{2}} $$

For the following exercises, solve the system by Gaussian elimination. $$ \begin{array}{c} 2 x+3 y=12 \\ 4 x+y=14 \end{array} $$

For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. $$ \frac{-24 x-27}{(6 x-7)^{2}} $$

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$ \left[\begin{array}{ccc} 1 & -2 & 3 \\ -4 & 8 & -12 \\ 1 & 4 & 2 \end{array}\right] $$

For the following exercises, use any method to solve the nonlinear system. $$ \begin{aligned} x^{2}+y^{2} &=9 \\ y &=3-x^{2} \end{aligned} $$

For the following exercises, find the determinant. $$ \left|\begin{array}{ccc|} -\frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ \frac{1}{5} & -\frac{1}{6} & \frac{1}{7} \\ 0 & 0 & \frac{1}{8} \end{array}\right| $$

For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. \(A=\left[\begin{array}{rr}2 & -5 \\ 6 & 7\end{array}\right], B=\left[\begin{array}{ll}-9 & 6 \\ -4 & 2\end{array}\right], C=\left[\begin{array}{ll}0 & 9 \\ 7 & 1\end{array}\right], D=\left[\begin{array}{rrr}-8 & 7 & -5 \\ 4 & 3 & 2 \\ 0 & 9 & 2\end{array}\right], E=\left[\begin{array}{rrr}4 & 5 & 3 \\ 7 & -6 & -5 \\ 1 & 0 & 9\end{array}\right]\) \(A+B-C\)

For the following exercises, solve the system by Gaussian elimination. $$ \begin{array}{l} -4 x-3 y=-2 \\ 3 x-5 y=-13 \end{array} $$