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Number of positive integral values of $p$ for which the system of equations $x + 2 y + z = p x$ , $- 3 x + p y = 2 z$ and $2 x - 2 y + z = - p z$ has a non-trivial solution, is

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$0$

$1$

$2$

$3$

answer is B.

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Detailed Solution

$|\begin{matrix} 1 - p & 2 & 1 \\ - 3 & p & - 2 \\ 2 & - 2 & 1 + p \end{matrix}| = 0 \Rightarrow p = 0, 3, - 3$

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