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Originally Posted by omert  I'm stuck with the problem:
1. does a linear transformations (T:R3 to R3) exists that follwing these terms:
T(1,0,1)=T(2,1,2)=T(0,1,1)=T(2,3,3)
if there is give an example for such transformation, if not explain why? |
Think about the linear transformation T(v)= (0,0,0) for all v.
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2. Let V,W be vector spaces over the same field, both from a finite dimension.
Let U sub space of V and dimU>=dimv-dimw
prove that there is a transformation T:V to W, that sustains kerT = U.
Thanks ahead
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Given any v in V, there exist vectors u, with u in U, and x such that v= u+ x with u in U. (choose a basis for both U, add vectors to make a basis for V and write v in terms of that basis). Define T(v)= x.