The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate row operations and describe the solution set of the original system.

(a).

Problem 2

Determine if the following systems are consistent. Do not completely solve the systems.

(a).

The system is consistent there is no contradiction.

Problem 3

Do the three planes , , and have at least one common point of intersection? Explain.

No they do not as the system required to find the common point of intersection is not consistent.

Problem 4

Mark each statement True or False.

[x] Elementary row operations on an augmented matrix never change the solution set of the associated linear system.
[ ] Two matrices are row equivalent if they have the same number of rows.
[ ] An inconsistent system has more than one solution.
[x] Two linear systems are equivalent if they have the same solution set.

Problem 5

Suppose , , , and are constants such that is not zero and the system below is consistent for all possible values of and . What can you say about the numbers , , , and ? Justify your answer.