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Saturday, 31 October

JEE Main · Maths · Matrices

Eigenvalue-Type Homogeneous Systems

JEE Main asked Eigenvalue-Type Homogeneous Systems once in the 108 shifts Lumi analysed, on 17 Mar 2021, Shift 2. It belongs to Cramer's Rule, in Matrices (Maths).

Updated 2026-10-24

Times asked
1
in 1 shift
Years
1 of 8
First asked
2021
the only year
Pattern
Gone quiet
asked once so far

Questions on this idea a shift, by year

2017–2026. Asked in 2021. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Determinant from ab=b and trace condition

Difficulty

Easy 0Medium 1Hard 0

1 of the 1 question had a numerical answer.

Every question

The question

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 17 Mar 2021, Shift 2 · Q90Let A=[abcd]A=\begin{bmatrix}a & b\\ c & d\end{bmatrix} and B=[αβ]≠[00]B=\begin{bmatrix}\alpha\\ \beta\end{bmatrix}\neq\begin{bmatrix}0\\ 0\end{bmatrix}…MediumNumerical value

Shift: 17 Mar 2021, Shift 2.

Same topic

Other ideas in Cramer's Rule

Cramer's Rule has 19 ideas JEE Main has asked; 6 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas