JEE Main201911 Jan 2019Morning ShiftMathematicsDeterminantsActual
If the system of linear equations 2 x+2 y+3 z=a3 x-y+5 z=bx-3 y+2 z=c where, a, b, care non-zero real numbers, has more than onc solution, then
Options
- Ab-c+a=0
- Bb-c-a=0
- Ca+b+c=0
- Db+c-a=0
Correct answer
B. b-c-a=0
Step-by-step solution
System of equations has more than one solution = ₁= ₂= ₃=0 for infinite solution aligned ₁ &= | array ccc a & 2 & 3 b & -1 & 5 c & -3 & 2 array |=a(13)+2(5 c-2 b)+3(-3 b+c) &=13 a-13 b+13 c=0 aligned i.c, a-b+c=0 or b-c-a=0