How to determine if a set represents a line, plane or hyperplane?

1.4k Views Asked by At

How do you approach a question that gives you a set and asked to determine if it represents a line, plane or hyperplane?

The Question:

https://www.dropbox.com/s/0gscqur18kqg3ma/SpanningQuestion.PNG

From what I gather this appears to be a plane because there are 3 columns. What I find confusing is why there is a 4th row and how to justify if it is a plane or not. There is an empty matrix that asks to provide a basis.

Any help or insight would be greatly appreciated!