Question Stem
Let $$\alpha, \beta$$ and $$\gamma$$ be real numbers such that the system of linear equations
$$x + 2y + 3z = \alpha$$
$$4x + 5y + 6z = \beta$$
$$7x + 8y + 9z = \gamma - 1$$
is consistent. Let $$\mid M \mid$$ represent the determinant of the matrix
$$M = \begin{bmatrix}\alpha & 2 & \gamma \\ \beta & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix}$$
Let P be the plane containing all those $$\left(\alpha, \beta, \gamma \right)$$ for which the above system of linear equations is consistent, and ๐ท be the square of the distance of the point (0, 1, 0) from the plane P.
The value of $$\mid M \mid$$ is ..........
Correct Answer: 0.95 - 1.05
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