D ) ?

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it is a diagonal matix(upper diagonal) so diagonal elements will be eigen values=2,2,2

Characteristics equation: $AX=\lambda X$

$\begin{bmatrix} 2 &1 &0 \\ 0 &2 &1 \\ 0& 0 &2 \end{bmatrix}$$\begin{bmatrix} x\\ y\\z \end{bmatrix}$=$\begin{bmatrix} 2x\\ 2y\\2z \end{bmatrix}$

On solving this we get z=0

Only option B has z=0

So option B is correct

Characteristics equation: $AX=\lambda X$

$\begin{bmatrix} 2 &1 &0 \\ 0 &2 &1 \\ 0& 0 &2 \end{bmatrix}$$\begin{bmatrix} x\\ y\\z \end{bmatrix}$=$\begin{bmatrix} 2x\\ 2y\\2z \end{bmatrix}$

On solving this we get z=0

Only option B has z=0

So option B is correct

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