GATE | GATE CS Mock 2018 | Question 45

Let


A = \begin{bmatrix}  4 & -2 & 1 \\  2 & 0 & 1 \\  2 & -2 & 3 \end{bmatrix} 

v1 = \begin{bmatrix}  1  \\  1  \\  0  \end{bmatrix} 

v2 = \begin{bmatrix}  0  \\  1  \\  2  \end{bmatrix} 

v3 = \begin{bmatrix}  1  \\  2  \\  -1  \end{bmatrix} 

v4 = \begin{bmatrix}  1  \\  1  \\  4  \end{bmatrix}

Which of the following statements is correct ?

(A) v1 and v2 are eigenvectors of A
(B) v1 and v3 are eigenvectors of A
(C) v2 and v3 are eigenvectors of A
(D) v3 and v4 are eigenvectors of A


Answer: (A)

Explanation: v1 and v2 are eigenvectors of A.
Av3 is not a multiple of v3 and Av4 is not a multiple of v4.



Option (A) is correct.


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