Determinant: For the system of linear equations x+3y+2z=7 x+lambda y+3z=8… | JEE Main 2021

JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 1

For the system of linear equations $x+3y+2z=7$ $x+\lambda y+3z=8$ $x-2y+7z=\mu$, which of the following statements is NOT true?

Determinant

The system has infinitely many solutions if $\lambda=2$ and $\mu=12$.The system has no solution if $\lambda=2$ and $\mu\neq12$.The system has a unique solution if $\lambda\neq2$ and $\mu=12$.The system has no solution if $\lambda\neq2$ and $\mu\neq12$.✓ Correct answer

Solution

Coefficient determinant $=5\lambda-10$, zero iff $\lambda=2$. For $\lambda\ne2$ the system has a unique solution for every $\mu$, so (C) is true and (D) (no solution when $\lambda\neq2$) is false. For $\lambda=2$: $E_2-E_1$ gives $-y+z=1$ and $E_3-E_1$ gives $-5y+5z=\mu-7$, so consistent iff $\mu=12$ (A, B true). NOT true: (D).

Determinant - JEE Mathematics question (JEE Main 2021 (Online) 3rd August Morning Shift)

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