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Technique

Cofactor expansion

det⁡A=∑jaijCij(any fixed row i)\det A = \sum_{j} a_{ij}C_{ij} \quad (\text{any fixed row } i)
aija_{ij}
the entry in row i, column j
CijC_{ij}
its cofactor, the signed minor

A determinant equals the sum of the products of the entries of any one row or column with their own cofactors.

99
questions use it
50
of them past-year
2017–2026
years it has appeared
44%
rated HARD
3
exams
Matrices & Determinants notesOpen all 99 in the paper builder

Used alongside

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

99 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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