linear algebra vectors problem

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mooshupork34

Junior Member
Joined
Oct 29, 2006
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72
Here are some vectors in a set, R4:

w1 = (1, -1, 1, 2), w2 = (1, 2, 1, 1), w3 = (-2, 2, -2, 4), w4 = (1, 1, -2, 1)

The question is which vectors in the set are parallel and why?
 
In general, two vectors u and v in a vector space are said to be parallel if u=kv, for some scalar k.

For example in R^2, <-4,2> = (-2) <2,-1>, so <-4,2> and <2,-1> are parallel.

Now look at your list. Are any of those vectors a real number times another one?
 
Hmm...

Okay, well
w1 to w4: there doesn't seem to be any scalar that retrieves the other one.
w1 to w2: there doesn't seem to be any.
w1 to w3: i tried -2, but that doesn't work because 2 * -2 = -4 and not 4
w2 to w3: there doesn't seem to be any.
w3 to w4: i tried -1/2, but that doesn't seem to work since 2 * -1/2 is -1 and not 1
w2 to w4: again there, doesn't seem to be any.

So I'm guessing there aren't any parallel vectors?
 
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