Find a matrix which is a Jordan canonical form for A

Question

Suppose A is an element of $M_{7x7} \mathbb{C}$ is a matrix with characteristic polynomial: x(A(t))=$(2-t)^2(3-t)^2(4-t)^3$ Suppose as well that:dim}N(A-2I) = 1 , dim N(A-3I) = 2,dim N(A-4I) = 1

Find a matrix which is a Jordan canonical form for A

Answer 1

Hint:

Each Jordan block corresponds to an eigenvector. You need $4$ Jordan blocks.

For example, $\begin{bmatrix} 2 & 1 \\ 0 & 2 \end{bmatrix}$ has $2$ as an eigenvalue and it has one independent eigenvector. Think of the other suitable Jordan blocks and put them together.