If $k$, $l$ and $n$ are integers such that $1 \leq k \leq l \leq n$, show that there exists an $n \times n$ matrix $A$ and an eigenvalue $\alpha$ of $A$ such that $k$ and $l$ are the geometric and algebraic multiplicities of $\alpha$ with respect to $A$.
I figured out that the following matrix formation an algebraic multiplicity $l$ for $\alpha$
\begin{bmatrix}
\lambda_1 & 0 & \dots & 0& 0&\dots &0 \\
0&\lambda_2 & \dots & 0& 0&\dots &0 \\
.\\
0 & 0 &\dots &\lambda_{n-k} & 0&\dots &0 \\
0 & 0 &\dots &0 & \alpha&\dots &0 \\
.\\
0 & 0 &\dots &0 & 0&\dots &\alpha \\
\end{bmatrix}
but I need help regarding the geometric multiplicity.