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GATE | GATE CS Mock 2018 | Question 45

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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)

v3 and v4 are eigenvectors of A
 

(B)

v2 and v3 are eigenvectors of A
 

(C)

v1 and v3 are eigenvectors of A
 

(D)

v1 and v2 are eigenvectors of A
 



Answer: (D)

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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Last Updated : 03 Jan, 2018
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