Exercise 5

For each of the questions below, provide a justification for your response.

1. What does the presence of a row whose entries are all zero in an augmented matrix tell us about the solution space of the linear system?

2. How can you determine if a linear system has no solutions directly from its reduced row echelon matrix?

3. How can you determine if a linear system has infinitely many solutions directly from its reduced row echelon matrix?

4. What can you say about the solution space of a linear system if there are more variables than equations and at least one solution exists?