sswann222
  • sswann222
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?
Mathematics
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sswann222
  • sswann222
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?
Mathematics
jamiebookeater
  • jamiebookeater
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TuringTest
  • TuringTest
do we know how many elements in each vector? is it n?
TuringTest
  • TuringTest
b) is yes either way...
sswann222
  • sswann222
first question: No we do not know how many elements. Just Xn and then we add Xn+1.

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TuringTest
  • TuringTest
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

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