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owlet
 one year ago
Spanning set & Linearly (In)dependent
Question below. I'm stuck. I don't know what's next...
owlet
 one year ago
Spanning set & Linearly (In)dependent Question below. I'm stuck. I don't know what's next...

This Question is Closed

amistre64
 one year ago
Best ResponseYou've already chosen the best response.12 vectors define a plane, a 2d object ... can a 2d object touch all of 3d space?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1and independant set is one in which each vector cannot be defined in terms of other vectors in the set

owlet
 one year ago
Best ResponseYou've already chosen the best response.0no? 2d can't span all 3d space, so it is not a spanning set of R^3? so since c2 needs c1, then it is linearly dependent?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1since 2,4,0 is not a scaled version of 2,1,3 the vectors are independant.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1one way to consider it is ... a v1 + b v2 = v3 for all vectors (v3) in R^3 in order to span (to cross over, to reach all points) of R^3, you have to be able to create them from the given conditions ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1a(2,1,3) + b(2,4,0) = (x,y,z) 2a + 2b = x a + 4b = y 3a + 0b = z can the vector (0,1,3) be obtained? 2a + 2b = 0; b=1 a + 4b = 1; 14 doest eqaul 1 3a + 0b = 3 ; a = 1

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1think of a piece of paper, you can draw 2 arrows on it that can be combined to reach all points in that paper ... but in order to get off of the paper you need to add a vector that is not contained on the paper ... a vector that points above/below it.

owlet
 one year ago
Best ResponseYou've already chosen the best response.0oh okay... i think i understand it better. two vectors = only spans a plane so if in case i'm given three vectors, there will be a possibility that they can span R^3 right?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1it requires n, independant vectors, to span R^n ... yes

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1... at least might need to be included for rigor

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1two independant vectors create a plane yes

owlet
 one year ago
Best ResponseYou've already chosen the best response.0for the linearly independent/dependent, dw:1443917976763:dw

owlet
 one year ago
Best ResponseYou've already chosen the best response.0oh i think it makes sense to me now

owlet
 one year ago
Best ResponseYou've already chosen the best response.0okay thank you again! :)
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