Determinant: The values of m,n , for which the system of equations x+y+z=4 ,… | JEE Main 2024

JEE Main 2024 (Online) 5th April Evening ShiftQuestion 1

The values of $m,n$, for which the system of equations $x+y+z=4$, $2x+5y+5z=17$, $x+2y+mz=n$ has infinitely many solutions, satisfy the equation :

Determinant

$m^{2}+n^{2}+mn=68$$m^{2}+n^{2}-mn=39$✓ Correct answer$m^{2}+n^{2}+m+n=64$$m^{2}+n^{2}-m-n=46$

Solution

The coefficient determinant $3m-6=0$ gives $m=2$; consistency ($x=1$, $y+z=3$ from the first two) gives $n=1+2\cdot3=7$. Then $m^2+n^2-mn=4+49-14=39$.

Determinant - JEE Mathematics question (JEE Main 2024 (Online) 5th April Evening Shift)

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