Practice questions CC-BY-NC

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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.