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Techniques of ROW REDUCTION can simplify the process of evaluating the determinant of a matrix. Replace row 2 with row 2 + k(row 1).
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Techniques of ROW REDUCTION can simplify the process of evaluating the determinant of a matrix
Replace row 2 with row 2 + k(row 1) When you replace a row of a matrix with itself plus a multiple of another row, the determinant does not change.
Replace row 2 with row 2 + k(row 1) When you interchange 2 rows of a matrix, the determinant changes by a factor of –1. This would not simplify the process of evaluating a determinant.
Replace row 1 with k(row 1) When you replace a row of a matrix with k times itself, the determinant changes by a factor of k. This would not simplify the process of evaluating a determinant.