Science:Math Exam Resources/Courses/MATH152/April 2022/Question A12/Statement

Consider the system of linear equations ${\textstyle Ax=b}$, where ${\textstyle A}$ is a ${\textstyle 5\times 7}$ matrix of real numbers, ${\textstyle b}$ is a ${\textstyle 5\times 1}$ vector of real numbers, and ${\textstyle x}$ is a ${\textstyle 7\times 1}$ vector of unknowns. Which of the following could describe the collection of all solutions ${\textstyle x}$? List all that are possible for some ${\textstyle A}$ and ${\textstyle b}$.

1. no solutions
2. precisely one solution
3. precisely 5 solutions
4. precisely 7 solutions
5. infinitely many solutions, forming a line
6. infinitely many solutions, forming a plane