Question

How do I know when two vectors are "linearly independent". For example a = <1,2,3,4> and b = <5,10,15,20>

Answer 1

so I've noticed a connection between determinants and cross product... The cross product tells me that axb = 0 when the two vectors are parallel.

Answer 2

I just can't remember what it means to say the two vectors are "linearly independent" or "linearly dependent". Just a concept question

Answer 3

I just figured out the answer to this question. Linear independence is when the two vectors cross resulting in a unique solution through a particular point and Linear "independence" is when the two vectors remain parallel and never cross resulting in infinitely many solutions to describe the vectors

Answer 4

Hence, if determinant or cross product is is zero the vectors are parallel or linearly dependent.....oh lol what I said above is false though ;0

Answer 5

If one vector is a multiple of another, then they are dependent and parallel.