Thread: 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

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.

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

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).

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

Originally Posted by skittle

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

Find the second derivative, then plug in zero.