Question

An indexed set of vectors { v1,v2,...,vp} is linearly dependent if

Answer 1

one of them can be made by combinations of the others

Answer 2

And by combination you mean elementary row operations.

Answer 3

Can anyone give me an example. That would be helpful.

Answer 4

v1 = 1,2

v2 = 2,4

Answer 5

Well yeah because they are multiples of each other.

Answer 6

I can cancel one and have the zero vector.

Answer 7

right, so they are actually both on the same line and one is dependant on the other in that regards; you can create one from a combonation of the others

Answer 8

3 vectors in a plane are linearly dependant since it only takes 2 vectors to reach every point

4 vectors in a cube are dependant since 3 vectors can reach every point in a cube

etc

Answer 9

Oh ok so as long as I can create a zero vector with the given vectors or if there is already a zero vector in the set I can say that the set of vectors are dependent.

Answer 10

Is this the only rule?

Answer 11

i wish it was the only rule; there is like a dozen of them that all really amount to the same thing said in a dozen different ways

Answer 12

Yeah I hear my prof said a couple but then I realized it led me to the same conclusion so I was just trying to make sure.

Answer 13

if the determinant = 0; its dependant

if the row reduction echelon form has a row or column of zeros; its dependant

if the the trivial solution is not the only solution to the zero vector, its dependant

....yada yada yada

Answer 14

oh i see lol @amistre64
If there is a zero row or vector and you have it in triangle form then the determinant will be zero. I see how things kind of repeat itself.