- #1

HmBe

- 45

- 0

## Homework Statement

## The Attempt at a Solution

For part ii) I wrote it out as a matrix, getting

\begin{array}{ccccccc}

0 & 0 & 0 & 0 & ... & 0 \\

0 & 0 & 2 & 0 & ... & 0 \\

0 & 0 & 0 & 6 & ... & 0 \\

. & . & . & . & . & . \\

0 & 0 & 0 & 0 & ... & N(N-2) \end{array}

So the rank = N-2 and the nullity = 2

However for part i) I'm not entirely sure how to go about it. Is it enough to show the map can be written as a matrix form, or do I need to show the additivity and scalar multiplication things hold over differentiation? Or is either ok?

Cheers.