Consider a matrix \(P\) whose only eigenvectors are the multiples of…

2018

Consider a matrix \(P\) whose only eigenvectors are the multiples of \(\begin{bmatrix} 1 \\ 4 \end{bmatrix}\).

Consider the following statements.

(I) \(P\) does not have an inverse

(II) \(P\) has a repeated eigenvalue

(III) \(P\) cannot be diagonalized

Which one of the following options is correct?

Answer: D. Only II and III are necessarily true

  1. A.

    Only I and III are necessarily true

  2. B.

    Only II is necessarily true

  3. C.

    Only I and II are necessarily true

  4. D.

    Only II and III are necessarily true

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Correct answer: D

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