3. Matrix Methods for Systems

Existence And Uniqueness Of Solutions — Quiz

Test your understanding of existence and uniqueness of solutions with 5 practice questions.

Practice Questions

Question 1

For a square system $A\mathbf{x}=\mathbf{b}$, what condition guarantees a unique solution?

Question 2

What does a row of the form $[0\ 0\ 0 \mid 5]$ in a row-reduced augmented matrix indicate?

Question 3

A consistent system has at least one free variable. What does that imply?

Question 4

If $A$ is invertible, what can you say about the system $A\mathbf{x}=\mathbf{b}$ for any vector $\mathbf{b}$?

Question 5

Two distinct lines in the plane intersect at exactly one point. How many solutions does the corresponding linear system have?