JEE Main 2018 · Mathematics · Matrices and Determinants · hard

For the system x+y+z=6, x+2y+3z=14, x+2y+λ z=μ to have infinitely many solutions, λ+μ must equal

Single correct option

For the system

x+y+z=6,\ x+2y+3z=14,\ x+2y+\lambda z=\mu

to have infinitely many solutions,

\lambda+\mu

must equal

Show answer and solution

Answer: (B) $17$

Subtracting the second equation from the third gives

(\lambda-3)z=\mu-14

. Infinitely many solutions need

\lambda-3=0

and

\mu-14=0

, i.e.

\lambda=3,\ \mu=14

. Hence

\lambda+\mu=17

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