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Technique

Row and column operations

RiRi+λRj    detA unchangedR_i \to R_i + \lambda R_j \;\Rightarrow\; \det A \text{ unchanged}
Ri,CiR_i, C_i
the i-th row and column

Adding a multiple of one row or column to another leaves the determinant unchanged, which is what makes a determinant collapsible before expansion.

71
questions use it
21
of them past-year
2017–2026
years it has appeared
35%
rated HARD
2
exams
Matrices & Determinants notesOpen all 71 in the paper builder

Used alongside

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

71 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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