JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let A be a

3\times3

real matrix such that

A\begin{pmatrix}1\\1\\0\end{pmatrix}=\begin{pmatrix}1\\1\\0\end{pmatrix}

;

A\begin{pmatrix}1\\0\\1\end{pmatrix}=\begin{pmatrix}-1\\0\\1\end{pmatrix}

and

A\begin{pmatrix}0\\0\\1\end{pmatrix}=\begin{pmatrix}1\\1\\2\end{pmatrix}

. If

X=(x_1, x_2, x_3)^{\mathrm{T}}

and I is an identity matrix of order 3, then the system

(A-2I)X=\begin{pmatrix}4\\1\\1\end{pmatrix}

has :

(1)no solution
(2)infinitely many solutionsOfficial answer
(3)unique solution
(4)exactly two solutions

Official answer

Option 2

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Parametrizing Infinite Solutions

Same topic in other shifts

All Cramer's Rule questions

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.