# Linear Transformations

1. May 16, 2005

### laminatedevildoll

I've uploaded a document which I am currently working on. I would like to verify if I am doing these problems correctly. Thank you.

In the first attachment (3.4b)
For 1.
a. 4x^3-2x
b. T(P)=0
ker T={C:C $$\in$$R}
Im T = {P|P is less than degree 3 or less}

c. T is not one to one because P is a constant. T is not onto because it's degree less than 3. I am not sure if I am proving this right. I'd appreciate some help.

For 2.
a. 1/5x^5-1/3x^3+C
b.
ker T={C:C $$\in$$R}
Im T = {P|P is less than degree 5 or less}
T is not one to one because C=0. But, T is on-to. How do I prove this?

In the second attachment (3.4a) part 4.
I proved that T is one to one because T(f)=T(g), f=g How do I prove that this is on-to?

#### Attached Files:

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• ###### 3-4a.pdf
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2. May 17, 2005

### laminatedevildoll

nvm, I understand it.