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

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.

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

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

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

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

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