I'm having trouble with these questions:

If given a linear system:

and

For which values of m and k (unique values or certain sets of values) are the following true:

1: The system has unique solutions

2: The system has no unique solutions

3: There are infinitely many solutions

Or, consider the system of three equations:

For what values of a are the same three conditions above satisfied?

Also, what techniques are used to do these questions in general?

Thanks for all the help in advance