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MathsJEE Main 23 Jan 2026, Shift 2·Q6·MCQ·Easy–moderate

Matrices & Determinants · Consistency of linear equations

The system of linear equations
x+y+z=62x+5y+az=36x+2y+3z=b\begin{align*} x + y + z &= 6\\ 2x + 5y + az &= 36\\ x + 2y + 3z &= b \end{align*}
has
  1. (1)unique solution for a=8a = 8 and b=16b = 16
  2. (2)infinitely many solutions for a=8a = 8 and b=14b = 14
  3. (3)infinitely many solutions for a=8a = 8 and b=16b = 16
  4. (4)unique solution for a=8a = 8 and b=14b = 14

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