GATE | GATE 2017 MOCK II | Question 30

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(A) 1
(B) 2
(C) 3
(D) 4


Answer: (B)

Explanation: Characteristic Equation is \left |A - \lambda I  \right | = 0 => \lambda^3 - 4*\lambda^2 + 5*\lambda -2 = 0=> \lambda = 1,1,2
Eigen vector for \lambda = 1

(A-I)X = 0 => \begin{bmatrix} 0 &3  &2 \\  0 &3  &2 \\  0 &-3  & -2 \end{bmatrix}\begin{bmatrix} x\\  y\\  z \end{bmatrix} = \begin{bmatrix} 0\\  0\\  0 \end{bmatrix}
Rank of the matrix (A-I) is 1 and number of unknown is 3.
Therefore, Number of linearly independent eigen vectors = 3-1=2


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