Consider a matrix P whose only eigenvectors are the multiples of $\left[ {\begin{array}{*{20}{c}}1\4\end{array}} \right]$.Consider the following statements. (I) P does not have an inverse(II) P has a repeated eigenvalue(III) P cannot be diagonalizedWhich one of the following options is correct?

Question

Consider a matrix P whose only eigenvectors are the multiples of $\left[ {\begin{array}{*{20}{c}}1\4\end{array}} \right]$.Consider the following statements. (I) P does not have an inverse(II) P has a repeated eigenvalue(III) P cannot be diagonalizedWhich one of the following options is correct?

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

Only I and III are necessarily true

TuteeHUB · Answer

Only II is necessarily true

TuteeHUB · Answer

Only I and II are necessarily true

TuteeHUB · Answer

Only II and III are necessarily true

1.	Consider a matrix P whose only eigenvectors are the multiples of \(\left[ {\begin{array}{*{20}{c}}1\\4\end{array}} \right]\).Consider the following statements. (I) P does not have an inverse(II) P has a repeated eigenvalue(III) P cannot be diagonalizedWhich 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
Answer» E.

Consider a matrix P whose only eigenvectors are the multiples of \(\left[ {\begin{array}{*{20}{c}}1\\4\end{array}} \right]\).Consider the following statements. (I) P does not have an inverse(II) P has a repeated eigenvalue(III) P cannot be diagonalizedWhich one of the following options is correct?

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