Question

Onto and one-to-one? I don't understand how you'd know if a transformation is one-to-one or onto?

Answer 1

Like lets say T:R^3 ---> R^3 is the rotation about the z axis through an angle of pi/4

Answer 2

>.> horizontal line test :D?

Answer 3

Um I don't think so this is linear algebra

Answer 4

It says like it's onto if the range is the entire codomain R^m that is every vector in R^m is the image of at least one vector in R^n someone want to explain what that means

Answer 5

one to one function means every element in domian should have only one single mapping,and onto means every element in the co domain must have one element mapped on it...
hope u understood

Answer 6

No I'm still kind of confused, do you mind doing my example?

Answer 7

How do you prove something is one to one T: R^n ---> R^m can m and n equal one another

Answer 8

This is an example of proving something one to one

http://answers.yahoo.com/question/index?qid=20110811010005AA77kii

All a bit .... I know but there u go.

Would imagine this is similar sort of thing..

Answer 9

nope nope we take the elements see....not the range

Answer 10

off u go then...:-)

Answer 11

Ahh okay I shall reread my textbook.. Thanks for your attempts

Answer 12

Really tiresome, just go back to definitions and proooove....