TITLE: How can I visualize independent and dependent set of vectors?
QUESTION [9 upvotes]: Can someone help me visualize those concepts? It will also help me understand it better.
Thanks :)

REPLY [2 votes]: Two parallel vectors are linearly dependent. Three vectors lying in a plane are linearly dependent. Four vectors lying in the same three-dimensional hyperplane are linearly dependent.
In n-dimensional space, you can find at most n linearly independent vectors.
Think of the vectors as rods with which you want to span up a tent: one rod gives you just a line, two rods give you a face. you need a third rod outside of that plane (linearly independent) to span up a volume. Any additional rods cannot span into a fourth dimension, so four rods in three dimensions must be linearly dependent.