7. Systems of Equations & Matrices

Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -7 times row 1 added to row 2

In Exercises 9-12, 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.

Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 2 times row 1 added to row 2

In Exercises 9 - 16, find the following matrices: b. A - B4 1 5 9A = B = 3 2 0 7

Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B4 1 5 9A = B = 3 2 0 7

Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 4 times row 1 added to row 2

In Exercises 9-12, 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.

In Exercises 9 - 16, find the following matrices: a. A + B3 1 1 2 - 3 6A = B = - 1 2 5 - 3 1 - 4

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B3 1 1 2 - 3 6A = B = - 1 2 5 - 3 1 - 4

In Exercises 9 - 16, find the following matrices: c. - 4A3 1 1 2 - 3 6A = B = - 1 2 5 - 3 1 - 4

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

In Exercises 13–18, perform each matrix row operation and write the new matrix.

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

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. A+D