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# A Question about linear transformations... watch

1. Define a linear transformation. T: --> R^2 by

T(p) = .

Find polynomials and in that span the kernel of T, and describe the range of T.

This is the definition of a linear transformation:

T(p+q) =

= +

= T(p) + T(q)

T(cp) =

= c= cT(p)

These are the polynomials and in :

T(p) = =

So p(0) = 0 and p(0) = 0...

I chose any two polynomials that met these requirments...so...

= x
= x^2

But I'm somewhat confused about the range...how can I find it?

2. You weren't asked to show that is linear so don't bother.

Your basis for the kernel is correct but needs more justification. Start with . Then , etc.

Range is , which is spanned by?

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