7. Systems of Equations & Matrices

What is the augmented matrix of the following system?

-3x + 5y = 2

6x + 2y = 7

In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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

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

Write the augmented matrix for each system of linear equations.

$\begin{cases}5x - 2y - 3z = 0 \\x + y = 5 \\2x - 3z = 4\end{cases}$

Use the given row transformation to change each matrix as indicated.

Write the augmented matrix for each system of linear equations.

$\begin{cases}2w + 5x - 3y + z = 2 \\3x + y = 4 \\w - x + 5y = 9 \\5w - 5x - 2y = 1\end{cases}$

Use the given row transformation to change each matrix as indicated.

Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

$\begin{bmatrix}5 & 0 & 3 & \vert & -11 \\0 & 1 & -4 & \vert & 12 \\7 & 2 & 0 & \vert & 3\end{bmatrix}$

Use the given row transformation to change each matrix as indicated.

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

Find the dimension of each matrix. Identify any square, column, or row matrices.

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

Use the given row transformation to change each matrix as indicated.

Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

$\begin{bmatrix}1 & 1 & 4 & 1 & \vert & 3 \\-1 & 1 & -1 & 0 & \vert & 7 \\2 & 0 & 0 & 5 & \vert & 11 \\0 & 0 & 12 & 4 & \vert & 5\end{bmatrix}$

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