Linear Transformation: Kernel, Range, and 1-1 Status

[kiaxus]

1. Find the kernel and range of the linear transformation. Indicate whether its 1-1, onto, both or neither



2. U: P2-----> R^2 defined by U(f(x)) = [f(1), f ' (1)]



3. To me by looking at the problem, it seems as if its going to be 1-1. As for solving this problem...I AM TOTALLY LOST! Please help. I just need to know how to begin, than I think I can get it from there.

 

[Cyosis]

When you're totally lost a good starting point would be the definition of the kernel and range of a linear transformation.

 

[vela]

What is P2? Is that the set of polynomials of degree 2 or less?

 

[kiaxus]

What is P2? Is that the set of polynomials of degree 2 or less?

P2 is a geographical meaning for a point or basis in linear transformation

 

[vela]

P2 is a geographical meaning for a point or basis in linear transformation

That makes absolutely no sense.

Let me ask it differently. What is the domain of U?

 

[kiaxus]

That makes absolutely no sense.

Let me ask it differently. What is the domain of U?

U = U(f(x))= [f(1), f ' (1)]

 

[Cyosis]

Kiaxus we have a template you are supposed to fill in. This template exists for a reason. Under the relevant equations you should list the definition of a kernel, the range and what the requirement is for a linear transformation to be one on one. This is where you need to start. Once you have looked up these definitions you will most likely realize where to start.

Vela asked you what the domain was, which you did not provide. What you have written down in #6 is an element from U's codomain.

To get rid of the confusion as to what P2 is (which is most likely the set of polynomials with degree two or less) could you give us an element of P2?