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 equations
\[
\begin{array}{l}
x+2 y+3 z=\alpha \\
4 x+5 y+6 z=\beta \\
7 x+8 y+9 z=\gamma-1
\end{array}
\]
is consistent. Let \( |M| \) represent the determinant of the matrix \( M=\left[\begin{array}{ccc}\alpha & 2 & \gamma \\ \beta & 1 & 0 \\ -1 & 0 & 1\end{array}\right] \) then value of \( |M| \) is
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