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  3. (1) suppose that v is a vector space and that s =

(1) Suppose that V is a vector space and that S = {u,v} is a...

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Advance Math

  1. (1) Suppose that V is a vector space and that S = {u,v} is a setof two vectors in V. Let w=u+v, let x=u+2v, and letT ={w,x} (sothatT is another set of two vectors in V ). (a) Show that if S islinearly independent in V then T is also independent. (Hint:suppose that there is a linear combination of elements of T that isequal to 0. Then ....). (b) Show that if S generates V then T alsogenerates V . (Hint: try solving for u and v in terms of w and x.).(c) Summarize the results of parts (a) and (b), correctly employingthe word “basis”.

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