Let α,β and γ be real numbers such that the system of linear equations x+2y+3z=α, 4x+5y+6z=β, 7x+8y+9z=γ−1 is consistent. Let ∣M∣ represent the determinant of the matrix
M=αβ−1210γ01
Let P be the plane containing all those (α,β,γ) 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?
a. The value of ∣M∣ is - - - -
b. The value of D is - - - -