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The number of linearly independent eigen vector of matrix A(3$\times$3) given as following

 a11=a22=2, a12=1, a13=a21=a23=a31=a32=0, a33=3

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Matrix looks like

$\begin{bmatrix} 2 &1 &0 \\ 0& 2 &0 \\ 0 &0 & 3 \end{bmatrix}$

Solving this we get $\lambda$ = 2,2,3 [since lower triangular Matrix]

Two linear independent solution i.e. for $\lambda$ = 2, and 3

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