Mathematics · Matrices

JEE Main 2026 — 23 January, Evening Shift — Question 6

The system of linear equations $x+y+z=6$ , $2 x+5 y+a z=36$ , $x+2 y+3 z=b$ has

Option A:
unique solution for $a=8$ and $b=16$
Option B:
infinitely many solutions for $a=8$ and $b=14$
Correct
Option C:
infinitely many solutions for $a=8$ and $b=16$
Option D:
unique solution for $a=8$ and $b=14$

Answer: B

Step-by-step solution

D= \begin{vmatrix} 1 & 1 & 1 \\ 2 & 5 & a \\ 1 & 2 & 3 \end{vmatrix} =0 \Rightarrow a=8

D_{1}= \begin{vmatrix} 6 & 1 & 1 \\ 36 & 5 & a \\ b & 2 & 3 \end{vmatrix} =0 \Rightarrow ab - 5b - 12a + 54 = 0

D_{2}= \begin{vmatrix} 1 & 6 & 1 \\ 2 & 36 & a \\ 1 & b & 3 \end{vmatrix} =0 \Rightarrow ab - 6a - 2b - 36 = 0

D_{3}= \begin{vmatrix} 1 & 1 & 6 \\ 2 & 5 & 36 \\ 1 & 2 & b \end{vmatrix} =0 \Rightarrow b=14

\text{For } a=8 \text{ and } b=14, \Rightarrow D_{1}=0 \text{ and } D_{2}=0

\Rightarrow D=D_{1}=D_{2}=D_{3}=0$$ $\Rightarrow$ Infinitely many solutions

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 23 January, Evening Shift
Subject: Mathematics
Chapter: Matrices
Topic: solving System of Linear Equations using Matrices

Let A= [beginarrayccc0 & 2 & -3 \\-2 & 0 & 1 \\3 & -1 & 0endarray ] and B be a matrix such that B( I- A)= I+ A . Then the sum of the…

The system of linear equations x+y+z=6 , 2 x+5 y+a z=36 , x+2 y+3 z=b… | JEE Main 2026 PYQ with Solution · DhiX AI