Determinant: Consider the following system of equations : x+2y-3z=a 2x+6y-11z=b… | JEE Main 2021

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 1

Consider the following system of equations : $x+2y-3z=a$ $2x+6y-11z=b$ $x-2y+7z=c$, where $a,b$ and $c$ are real constants. Then the system of equations :

Determinant

has a unique solution for all $a,b$ and $c$has a unique solution when $5a=2b+c$has infinite number of solutions when $5a=2b+c$✓ Correct answerhas no solution for all $a,b$ and $c$

Solution

Coefficient determinant $=0$ with rank 2; left null vector is $(-5,2,1)$, so the consistency condition is $-5a+2b+c=0$, i.e. $5a=2b+c$. When it holds, rank (coefficient) $=$ rank (augmented) $=2<3$: infinitely many solutions; otherwise no solution. Option (C).

Determinant - JEE Mathematics question (JEE Main 2021 (Online) 26th February Evening Shift)

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