Past exam of the year 1 of the computer science course of the University of Oxford / 2003 / Calculus, probability, linear algebra, discrete mathematics, logic and proof, and models of computation / 4 / a / ii

For a square matrix, the corresponding changes in its determinant are

R_{i} \leftrightarrow R_{j} R_{i} \leftarrow c R_{i} R_{i} \leftarrow R_{i} + c R_{j} : det ⟼ - det, : det ⟼ c det, : det ⟼ det .

These follow respectively from the alternating property, multilinearity in the rows, and the fact that a determinant with two equal rows vanishes.

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