1. ## Linear transformation

How do you find a basis for Ker(φ), a basis for Im(φ), the dimensions of the kernel, image and domain of φ for the following linear transformation.

φ : P4 -> R given by φ(p(x)) = p′′(0), where p′′(x) denotes the second derivative

2. Originally Posted by skittle
How do you find a basis for Ker(φ), a basis for Im(φ), the dimensions of the kernel, image and domain of φ for the following linear transformation.

φ : P4 -> R given by φ(p(x)) = p′′(0), where p′′(x) denotes the second derivative
What would a generic P4 polynomial look like? Then apply the transformation.

3. A generic P4 would look like a4x^4+a3x^3+a2x^2+a1x+a0. How would I then apply the transformation?

4. Originally Posted by skittle
A generic P4 would look like a4x^4+a3x^3+a2x^2+a1x+a0. How would I then apply the transformation?
By what you wrote, it says take p''(0).

5. So I would make the x's to be zeros?

6. Originally Posted by skittle
So I would make the x's to be zeros?
Find the second derivative, then plug in zero.