Question
If the system of equations 3 x+y+4 z=3 2 x+ y-z=-3 x+2 y+z=4 has no solution, then the value of is equal to :
JEE Main
Mathematics
Determinants
2026
JEE Main 2026 (21 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 19
- B. 4
- C. 13
- D. 23
Answer
A. 19
Step-by-step solution
For no solution = 0 vmatrix 3 & 1 & 4 \\ 2 & & -1 \\ 1 & 2 & 1 vmatrix = 0 3( + 2) + 1(-1 - 2) + 4(4 - ) = 0 19 - = 0 = 19 & for = 19 _x = vmatrix 3 & 1 & 4 \\ -3 & 19 & -1 \\ 4 & 2 & 1 vmatrix = 3(21) + 1(-1) + 4(-82) 0 no solution for = 19
Related: Mathematics — Determinants · All PYQ Banks