7. Systems of Equations & Matrices

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

In Exercises 19–20, a few steps in the process of simplifying the given matrix to row-echelon form, with 1s down the diagonal from upper left to lower right, and 0s below the 1s, are shown. Fill in the missing numbers in the steps that are shown.

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

Let and . Solve each matrix equation for X. 2X + A = B

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. -5(A+D)