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sswann222
 4 years ago
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?
sswann222
 4 years ago
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?

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0do we know how many elements in each vector? is it n?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0b) is yes either way...

sswann222
 4 years ago
Best ResponseYou've already chosen the best response.0first question: No we do not know how many elements. Just Xn and then we add Xn+1.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0well 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
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