# Practice questions

1. Let $(v_1, v_2, v_3)$ be a basis for $\mathbb R^3$. If $T \in \mathcal L(\mathbb R^3)$ is such that $Tv_i = 0$ for $i=1,2,3$, how many linearly independent eigenvectors does $T$ have?
• ANSWER: (D). $T$ is clearly the zero operator, for which every vector in $\mathbb R^3$ is an eigenvector. Since the dimension is 3, there are 3 linearly independent eigenvectors.