HOw do I know if a vector i linearlally independent or depenendent?

Question

I am lost completely

umm I hears something about the columns - Rank= 0 then it's independent else its dependent


idk how to solve or what am I supposed to do exactly??

what is it?

confused here

Answer 1

A set of vectors spanning a certain space are a set of inde
pendent vectors if it's impossible to write any one vector in
terms of the others. Just another way of saying 3 points
define a plane as long as they don't fall on a straight line.

Answer 2

First, the word is LINEARLY, not linear-lally. Well, I heard something about that also, but you have a book to explain it. Conceptually, if you have a "n-dimensional space", you need to have a minimum of n linearly-independent vectors to define any point in that space. Such a vector CANNOT be formed from the addition or subtraction of any or all other vectors or of their multiples.