Find all invariant subspace of $A$ Consider a matrix mapping $A: V \to V$ for a vertor space V. Matrix $A$ has 3 eigenvalues are distinct : $\lambda_1,\lambda_2,\lambda_3$ and $v_1,v_2,v_3$ are vectors-corresponding .Find all invariant subspace of  $A$

Hint: note that each $\text{span}(v_i)$ is a invariant vector space.
Also note that $\{0\}$ and $V$ are invariant subspaces. Furthermore note that if $A$ is an invariant subspace and $B$ is an invariant subspace then so is $A + B$.
