7. Systems of Equations & Matrices

Find the following matrices: - 3A + 2B

$A = \begin{bmatrix}3 & 1 & 1 \\-1 & 2 & 5\end{bmatrix}, B = \begin{bmatrix}2 & -3 & 6 \\-3 & 1 & -4\end{bmatrix}$

In Exercises 9 - 16, find the following matrices: c. - 4A

Write the augmented matrix for each system and give its dimension. Do not solve.

2x + y + z - 3 = 0

3x - 4y + 2z + 7 = 0

x + y + z - 2 = 0

Perform each matrix row operation and write the new matrix.

$\begin{bmatrix}2 & -6 & 4 & \vert & 10 \\1 & 5 & -5 & \vert & 0 \\3 & 0 & 4 & \vert & 7\end{bmatrix}\quad \frac{1}{2}R_1$

Write the augmented matrix for each system and give its dimension. Do not solve. 4x - 2y + 3z - 4 = 0 3x + 5y + z - 7 = 0 5x - y + 4z - 7 = 0

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

In Exercises 9 - 16, find the following matrices: a. A + B

In Exercises 9 - 16, find the following matrices: c. - 4A

Perform each matrix row operation and write the new matrix.

$\begin{bmatrix}1 & -3 & 2 & \vert & 0 \\3 & 1 & -1 & \vert & 7 \\2 & -2 & 1 & \vert & 3\end{bmatrix}\quad -3R_1 + R_2$

Write the system of equations associated with each augmented matrix . Do not solve.

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. D-A

Perform each matrix row operation and write the new matrix.

$\begin{bmatrix}1 & -1 & 1 & 1 & \vert & 3 \\0 & 1 & -2 & -1 & \vert & 0 \\2 & 0 & 3 & 4 & \vert & 11 \\5 & 1 & 2 & 4 & \vert & 6\end{bmatrix}\quad\begin{array}{l}-2R_1 + R_3 \\-5R_1 + R_4\end{array}$

Write the system of equations associated with each augmented matrix . Do not solve.

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. 3A+2D