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

GATE · 2018 · CS · Computer Science & IT

Consider a matrix PP whose only eigenvectors are the multiples of [14]\begin{bmatrix} 1 \\ 4 \end{bmatrix}.

Consider the following statements.

(I) PP does not have an inverse

(II) PP has a repeated eigenvalue

(III) PP cannot be diagonalized

Which one of the following options is correct?

  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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