As in Exercise 17, describe the solutions of the following system in parametric vector form, and provide a geometric comparison with the solution set in Exercise 6.

Exercise 17:

Follow the method of Example 3 to describe the solutions of the following system in parametric vector form. Also, give a geometric description of the solution set and compare it to that in Exercise 5.

Example 3: Describe all solutions of Ax = b, where

Exercise 5:

In Exercises 5 and 6, follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in parametric vector form.

Example 1: Determine if the following homogeneous system has a nontrivial solution. Then describe the solution set.

Example 2: A single linear equation can be treated as a very simple system of equations. Describe all solutions of the homogeneous “system”

Exercise 6:

Follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in parametric vector form.

Example 1: Determine if the following homogeneous system has a nontrivial solution. Then describe the solution set.

Example 2: A single linear equation can be treated as a very simple system of equations. Describe all solutions of the homogeneous “system”