Consider the linear systems with the following augmented matrices. In which case does the system have exactly one solution?

Which of the following matrices is in row-echelon form?

Let be a solution set to the equation . When viewing as the vector equation of a line in , what is the direction vector of this line?

Remark: If (meaning and are parallel) and is a direction vector of a line , then is also a direction vector of .

How many free parameters are needed to solve the equation ?

Let be a constant. How many solutions does the following system have?

Under what condition on does the following system have exactly 1 solution?

How many free parameters are there in the solution to the linear system with the following augmented matrix?

Consider the linear systems with the following augmented matrices. In which case does the system have exactly one solution?

Let be constants. Under what condition (on ) does the following system have infinitely many solutions?

(a)       (b)      (c)