I'm having problem regarding the Evaluation of a determinant. Can anyone explain me if there are any rules regarding row operations? I mean which row should I evaluate first?
2026-04-02 01:40:00.1775094000
Evaluating Determinants using elementary operations
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The determinant of a matrix can be evaluated by expanding along a row or a column of the matrix. You will get the same answer irregardless of which row or column you choose, but you may get less work by choosing a row or column with more zero entries. You may also simplify the computation by performing row or column operations on the matrix first. You then need to know what these operations on the matrix do to the determinant.
(1) If you multiply a row or column of the matrix with a constant, the determinant is multiplied with the same constant.
(2) If you let two rows (or two columns) switch place, the determinant changes sign.
(3) If you add a multiple of one row (or column) to another row (or column), the determinant is unchanged.
Property (3) is really the most important here, because it can be used with little effort to produce more zero entries in the matrix.