clarify pleasu

[Zebra]

linearly dependent.. (2 vectors adding up to another vector?? OR 3 vectors adding up to zero?)

i.e) there are 3 vectors a,b,c

ma + nb = c or ma + nb + zc =0

linearly independent (2 vectors NOT adding up to another vector??? OR the sum of 3 vectors don't equal zero??)


AND

can anyone define what a rhombus, parallelogram , kite , square ,rectangle is?

[AleksIlia]

Linearly dependent pretty much means that a vector from a set of vectors can be written terms of others afaik, ie ma + nb = c, rhombus is a pushed over square is what I was told. Rectangle has 2 sets of parallel vectors with different magnitude and adjacent sides are at right angles, only need to show one right angle for proofs

[Mao]

linearly dependent.. (2 vectors adding up to another vector?? OR 3 vectors adding up to zero?)

i.e) there are 3 vectors a,b,c

ma + nb = c or ma + nb + zc =0

linearly independent (2 vectors NOT adding up to another vector??? OR the sum of 3 vectors don't equal zero??)


AND

can anyone define what a rhombus, parallelogram , kite , square ,rectangle is?

For non-zero vectors, the prior is fine. But a rigorous definition requires the latter. If one of the vector is a zero vector, then the whole set is L.D., however the first equation does not capture this behaviour.

[Zebra]

:S i saw a question which told me that there are three vectors which are linearly dependent.
a= i,j,k with real number coeffs, b= i,j,k with real number coeffs. c= i,j,k with real number coeffs but are unknown.

i was asked to find the unknown values (that is, the coeffs of vector c)

as usual, i did ma+nb+zc =0 but then this felt wrong so i did
ma + nb = c

but then, this is what they did.

a+b=c (there was no m,n)
i find the questions very inconsitent with what they do....

[dc302]

Could you post the exact question? And was each coeff in c unknown, or only say, 2?

[Zebra]

i can't find the question but could you please clarify which one to stick to?

ma + nb = c or ma + nb + zc =0

AND

in linearly independent situations you just gotta show that
coeffs equal to zero?

far out so confusing!

[dc302]

I was asking because it may have asked you to find a linearly dependent vector. Usually, you would go an + bm = c, but if they just asked you to find a single vector, then you could definitely just get c = a + b. You could even have c = a, or c = b etc (which is why I think that would be a silly question).
Of course, otherwise you would need c = am + bn.

To show they are linearly independent, you need to show that:

If an+bm+cz=0, then m=n=z=0.

[Zebra]

I was asking because it may have asked you to find a linearly dependent vector. Usually, you would go an + bm = c, but if they just asked you to find a single vector, then you could definitely just get c = a + b. You could even have c = a, or c = b etc (which is why I think that would be a silly question).
Of course, otherwise you would need c = am + bn.

To show they are linearly independent, you need to show that:

If an+bm+cz=0, then m=n=z=0.

yeah you are spot on with the linearly dependent question.
BUT why? why don't we make use of m,n factors?

this is really important because depending on whether you use the factors or not, you get a different answer.
if i recall correctly, the question wanted me to fine the ratio of m and n (m/n) :S

[dc302]

I'm pretty sure they can't possibly ask you to find both c and m/n if c is 100% arbitrary. Why? Because then there are an infinite number of possible c's and so there would be way more than one answer. So unless you give me the full question I can't really help you.


edit: Actually, if they asked you to find the ratio of m and n, then you must have been required to use m and n in the first place. So I don't see how they could have simply added a and b, with no m and n, and then expect you to find the ratio of the non-existent m and n.