Consider the system of linear equations in x, y, z: x + 2y + tz = 0, 6x + y + 5tz = 0, 3x + t²y + f(t)z = 0, where f: R → R is a differentiable function. If this system has infinitely many solutions for all t R, then f

(B) is strictly increasing on R

(C) is strictly decreasing on R

Matrices and Determinants: JEE Main 2026 Mathematics question

JEE Main 2026 · 5 Apr, Morning shift · Q4

JEE Main 20265 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Consider the system of linear equations in

x, y, z

x + 2y + tz = 0

6x + y + 5tz = 0

3x + t^2y + f(t)z = 0

, where

f: \mathbb{R} \to \mathbb{R}

is a differentiable function. If this system has infinitely many solutions for all

t \in \mathbb{R}

, then

f