Urgent question! Basis of a vector space!
How do I find out if a set of vector is a basis of a vector space???
If I have L((1,1,0);(0,1,1)) how do I know if these other vectors are a basis of it?
-(1,0,0)
-((1,1,0);(0,1,1))
-((0,1,1);(1,1,-1))

Question

Urgent question! Basis of a vector space!
How do I find out if a set of vector is a basis of a vector space???
If I have L((1,1,0);(0,1,1)) how do I know if these other vectors are a basis of it?
-(1,0,0)
-((1,1,0);(0,1,1))
-((0,1,1);(1,1,-1))

amistre64 · Answer

a basis simply defines the minimum number of vectors needed to define a linear combination of them to hit all points in the space.

amistre64 · Answer

if you have say 4 vectors:  a,b,c,d  but b and d can be defined using some combination of a and c,  say:  b = 0a+3c,  and d=2a-c;  then the basis for the vector contained in the space can be defined in terms of a and c only.

anonymous · Answer

And how do I apply these concepts on the exercise?

anonymous · Answer

Thanks for helping me too :)

anonymous · Answer

Ah ok, now I get it. Thanks again :)

amistre64 · Answer

site hasnt been playing right for me.  but yeah, if L takes 2 vectors to reach all of the point in its space, then if im reading the options correctly; 1 vector is not going to work for a basis.  any 2 nonparallel vectors within the space would work as a basis for the space.  Just see if the the options are within the space and not parallel to each other.