let X1,X2,....Xn be linearly independent vectors in a vector space V.
(a) if we add a vector Xn+1 to the collection, will we still have a linearly independent collection of vectors?

(b) if we delete a vector, Xn, from our collection, will we still hav a linearly independent collection of vectors?

Question

let X1,X2,....Xn be linearly independent vectors in a vector space V.
(a) if we add a vector Xn+1 to the collection, will we still have a linearly independent collection of vectors?

(b) if we delete a vector, Xn, from our collection, will we still hav a linearly independent collection of vectors?

turingtest · Answer

do we know how many elements in each vector? is it n?

turingtest · Answer

b) is yes either way...

sswann222 · Answer

first question: No we do not know how many elements. Just Xn and then we add Xn+1.

turingtest · Answer

well that is strange, because it depends on what vector you have
say we have (1,0,0) and (0,1,0) 
if we add (2,0,0) then it is no longer linearly dependent
if we add (0,0,1) then it is still linearly dependent