(a) A set of vectors { x 1 , ... , X n ) in a vector...
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(a) A set of vectors { x1, ... , Xn) in a vector space V over a division ring R is linearly dependent if and only if some xk is a linear combination of the preceding xi.
(b) If { x1,X2,x3} is a linearly independent subset of V, then the set { x1 + x2, x2 + x3, x3 + x1} is linearly independent if and only if Char R ≠ 2.
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ANSWER a This statement is true To prove the forward direction suppose that the set of vectors x1 xn is linearly dependent Then there exist scalars a1 ...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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