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Property

Non-trivial solutions of a homogeneous system

AX=O has XO    Δ=0AX = O \text{ has } X \neq O \iff \Delta = 0
Δ\Delta
the coefficient determinant
OO
the zero column

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

24
questions use it
2
of them past-year
2023–2025
years it has appeared
38%
rated HARD
2
exams
Matrices & Determinants notesOpen 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.

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

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