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GATE | GATE 2017 MOCK II | Question 30

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marix (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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Last Updated : 14 Feb, 2018
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