Property

Non-trivial solutions of a homogeneous system

AX = O \text{ has } X \neq O \iff \Delta = 0

$\Delta$: the coefficient determinant
$O$: the zero column

A homogeneous system has a solution other than all zeros exactly when its coefficient determinant vanishes.

questions use it

of them past-year

2023–2025

years it has appeared

38%

rated HARD

exams

Matrices & Determinants notes Open all 24 in the paper builder

Used alongside

How often each of these appears in the same solution as this one.

24 questions whose solution uses this

Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.

Filter

Showing 24 of 24 questions — easiest first, then oldest paper first.

#1NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#2NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#3NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#4NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#5NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#6NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#7NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#8NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#9NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#10NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#11NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#12NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#13NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#14NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#15NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#16NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#17NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#18NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#19NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#20NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#21NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#22NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#23MHT-CET → Maths → Determinants and Matrices → Systems of Linear Equations and Symmetric, Skew-Symmetric Matrices
Strategy Concept notes
#24MHT-CET → Maths → Determinants and Matrices → Systems of Linear Equations and Symmetric, Skew-Symmetric Matrices
Strategy Concept notes

Every identity this chapter tests, with its own question set.

All Matrices & Determinants formulas