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

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

Mathematics
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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

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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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