JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

For the system to have infinitely many solutions, = 0 and _x = _y = _z = 0. = vmatrix 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & vmatrix = 1(2 - 9) - 1( - 3) + 1(3 - 2) = 2 - 9 - + 3 + 1 = - 5 Setting = 0 gives = 5. Now, calculating _z: _z = vmatrix 1 & 1 & 5 \\ 1 & 2 & 9 \\ 1 & 3 & vmatrix = 1(2 - 27) - 1( - 9) + 5(3 - 2) _z = 2 - 27 - + 9 + 5 = - 13 Setting _z = 0 gives = 13. For = 5 and = 13, we can verify that _x = 0 and _y = 0 as well. Therefore, + = 5 + 13 = 18. Answer: 18