Let \( \alpha, \beta \) and \( \gamma \) be real numbers such that the system of linear equation... VIDEO
Let \( \alpha, \beta \) and \( \gamma \) be real numbers such that the system of linear equation
\[
\begin{array}{l}
x+2 y+3 z=\alpha \\
4 x+5 y+6 z=\beta \\
7 x+8 y+9 z=\gamma-1
\end{array}
\]
is consistent. Let \( |M| \) represent the determinant of the matrix
\[
M=\left[\begin{array}{ccc}
\alpha & 2 & \gamma \\
\beta & 1 & 0 \\
-1 & 0 & 1
\end{array}\right]
\]
Let \( P \) be the plane containing all those \( (\alpha, \beta, \gamma) \) for which the above system of linear equations is consistent, and \( D \) be the square of the distance of the point \( (0,1,0) \) from the plane \( P \).
The value of \( |M| \) is
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