Q33Section B (Section B)33 of 60

Matrix whose every vector is an eigenvector

Let $P$ be a $2\times2$ real matrix such that every non-zero vector in $\mathbb R^2$ is an eigenvector of $P$ . Suppose that $\lambda_1$ and $\lambda_2$ denote the eigenvalues of $P$ and $P\begin{bmatrix}\sqrt2\\\sqrt3\end{bmatrix}=\begin{bmatrix}2\\t\end{bmatrix}$ for some $t\in\mathbb R$ . Which of the following statements is (are) TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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