JEE Main 2019 · Mathematics · Matrices and Determinants · hard

For real constants λ,μ, the linear system x+y+z=6, x+2y+3z=10, x+2y+λ z=μ has infinitely many solutions. The value of λ+μ is

Single correct option

For real constants

\lambda,\mu

, the linear system

x+y+z=6,\ x+2y+3z=10,\ x+2y+\lambda z=\mu

has infinitely many solutions. The value of

\lambda+\mu

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Answer: (A) 13

Subtracting the second equation from the third gives

(\lambda-3)z=\mu-10

. For infinitely many solutions this must hold for all

z

on the solution line, so

\lambda=3

and

\mu=10

. Hence

\lambda+\mu=13

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