Perform each matrix row operation and write the new matrix.

$\begin{bmatrix} 1 & 2 & 2 & \vert & 2 \\ 0 & 1 & -1 & \vert & 2 \\ 0 & 5 & 4 & \vert & 1 \end{bmatrix} -5R_2 + R_3$

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

$\{\begin{array}{c}x+2y+3z=-5\\ 2x+y+z=1\\ x+y-z=8\end{array}$

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

$\{\begin{array}{c}3x_1+5x_2-8x_3+5x_4=-8\\ x_1+2x_2-3x_3+x_4=-7\\ 2x_1+3x_2-7x_3+3x_4=-11\\ 4x_1+8x_2-10x_3+7x_4=-10\end{array}$

Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D

Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. BD

Evaluate each determinant.

Evaluate each determinant.

Use Cramer's Rule to solve each system.

$\{\begin{array}{c}7x+2y=0\\ 2x+y=-3\end{array}$