Determinant: The following system of linear equations 7x+6y-2z=0 , 3x+4y+2z=0 ,… | JEE Main 2020

JEE Main 2020 (Online) 9th January Evening ShiftQuestion 1

The following system of linear equations $7x+6y-2z=0$, $3x+4y+2z=0$, $x-2y-6z=0$, has :

Determinant

no solution.only the trivial solution.infinitely many solutions, $(x,y,z)$ satisfying $y=2z$.infinitely many solutions, $(x,y,z)$ satisfying $x=2z$.✓ Correct answer

Solution

$\begin{vmatrix}7&6&-2\\3&4&2\\1&-2&-6\end{vmatrix}=7(-24+4)-6(-18-2)-2(-6-4)=-140+120+20=0$, so nontrivial solutions exist. Solving: $x+(-2)y-6z=0$ and $3x+4y+2z=0$ gives $(x,y,z)\propto(2,-2,1)$, i.e. $x=2z$, $y=-2z$. So infinitely many solutions with $x=2z$. Option (D).

Determinant - JEE Mathematics question (JEE Main 2020 (Online) 9th January Evening Shift)

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