Let the system of linear equations x + y + α z = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x ^, y ^, z ^). If (α, x ^), (y ^, α) and (x ^, - y ^) are collinear points, then the sum of absolute values of all possible values of α is

Matrices and Determinants: JEE Main 2022 Mathematics question

JEE Main 2022 · 24 Jun, Evening shift · Q4609

JEE Main 202224 Jun, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

Let the system of linear equations x + y +

\alpha

z = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x

^ *

, y

^ *

, z

^ *

). If (

\alpha

, x

^ *

), (y

^ *

\alpha

) and (x

^ *

-

^ *

) are collinear points, then the sum of absolute values of all possible values of

\alpha