I have been asked to find all invariant subspaces of the linear map given by the Jordan Block matrix: $$J_{2}(\lambda)\in\mathbb{R}^{2x2}, \quad\lambda\in\mathbb{R}$$
I know that $$J_{2}(\lambda)=\left( \begin{array}{cc} \lambda & 1 \\ 0 & \lambda \end{array} \right)$$ but I don't clearly understand what I'm being asked to do. How would you solve this problem?