ONTO - Surjection

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Hi :smile: I'm new on these forums, and not only is this my first post, but this is also my first thread.

The following is not a homework question, but a question I found. However, I have no idea how to do this. I would appreciate it if someone could help me. Please click on the following link :tongue:

Untitled-2.jpg
 

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Welcome to the forums! To show in general that a map T is surjective you need to show that for every element in v in the range, there exists an element w in the domain such that T(w) = v. With a linear map, it is a little easier since you can deal with a basis. To show that a linear map is surjective, it is sufficient to show that a basis for the range is in the image set. In the problem you linked to, you can see that (1,1) and (1,2) are in the range. Do those two vectors form a basis for R^2? If so, the map is surjective.
 
  • #3
Welcome to the forums! To show in general that a map T is surjective you need to show that for every element in v in the range, there exists an element w in the domain such that T(w) = v. With a linear map, it is a little easier since you can deal with a basis. To show that a linear map is surjective, it is sufficient to show that a basis for the range is in the image set. In the problem you linked to, you can see that (1,1) and (1,2) are in the range. Do those two vectors form a basis for R^2? If so, the map is surjective.
Thank you very much eok20. I think I finally understand :approve:

I really appreciate your help!
 

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