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Matrices and Determinants question

2021 · Shift 1 · Q27
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  5. /2021 · Shift 1 · Q27

Matrices and Determinants question

2021 · Shift 1 · Q27

JEE AdvancedMathematicsMatrices and DeterminantsNumerical+2 / −1
Let α\alphaα, β\betaβ and γ\gammaγ be real numbers such that the system of linear equations x + 2y + 3z =α\alphaα 4x + 5y + 6z =β\betaβ 7x + 8y + 9z =γ−\gamma -γ− 1 is consistent. Let | M | represent the determinant of the matrix M=[α2γβ10−101]M = \left[ {\begin{matrix} \alpha & 2 & \gamma \\ \beta & 1 & 0 \\ { - 1} & 0 & 1 \\ \end{matrix} } \right]M=​αβ−1​210​γ01​​ Let P be the plane containing all those (α\alphaα, β\betaβ, γ\gammaγ) 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 D is ‾\underline{\hspace{2cm}}​.
Numerical answer
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