Practice questions

Some student-created multiple choice questions, with solutions and explanations provided.

Under construction

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?
   • (A) 0
   • (B) 1
   • (C) 2
   • (D) 3
   • (E) Impossible to determine without further information
   • 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.