Question
The system of linear equations x+y+z=6 2 x+5 y+a z=36 x+2 y+3 z=b has
JEE Main
Mathematics
Determinants
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. unique solution for a=8 and b=16
- B. infinitely many solutions for a=8 and b=16
- C. unique solution for a=8 and b=14
- D. infinitely many solutions for a=8 and b=14
Answer
D. infinitely many solutions for a=8 and b=14
Step-by-step solution
Coefficient matrix determinant: = 1(15-2a) - 1(6-a) + 1(4-5) = 8 - a. For a = 8, = 0, so unique solution is not possible. With a = 8: R_2 - 2R_1 gives 3y + 6z = 24 y + 2z = 8. R_3 - R_1 gives y + 2z = b - 6. For consistency: b - 6 = 8 b = 14. When a = 8, b = 14: the system has infinitely many solutions.
Related: Mathematics — Determinants · All PYQ Banks