Section: Engineering Mathematics | Marks: 2
Let $R$ be an $n \times n$ nonsingular matrix. Let $P$ and $Q$ be two $n \times n$ matrices such that $Q = R^{-1}PR$. If $x$ is an eigenvector of $P$ corresponding to a nonzero eigenvalue $\lambda$ of $P$, then
- A. $Rx$ is an eigenvector of $Q$ corresponding to the eigenvalue $\lambda$ of $Q$
- B. $Rx$ is an eigenvector of $Q$ corresponding to the eigenvalue $\frac{1}{\lambda}$ of $Q$
- C. $R^{-1}x$ is an eigenvector of $Q$ corresponding to the eigenvalue $\frac{1}{\lambda}$ of $Q$
- D. $R^{-1}x$ is an eigenvector of $Q$ corresponding to the eigenvalue $\lambda$ of $Q$