Kernel and range

I don't understand this kernel and range stuff.

Determine the kernel and range of each of the following linear transformations from R3 into R3.
(a) L(x) = (x3, x2, x1)^T

(b) L(x) = (x1, x1, x1)^T

And determine the kernel and range of each of the following linear transformations from P3 into P3.
(a) L(p(x)) = xp'(x)

(b) L(p(x)) = p(0)x + p(1)

Thank you!

Solution Summary

This shows how to find kernel and range of linear transformations.