 Solution

ID: 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/solution

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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