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?
- A.
Only I and III are necessarily true
- B.
Only II is necessarily true
- C.
Only I and II are necessarily true
- D.
Only II and III are necessarily true
Attempted by 85 students.
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Correct answer: D
