Math Course Help With Properties Of Determinants

3.6.3 Properties of determinants:

• i) The value of a determinant remains unchanged if its rows and columns are interchanged.
• ii) If two rows or columns of a determinant are interchanged, then the determinant retains its absolute value but its sign is changed.
• iii) If any two rows or columns of a determinant are identical then its value is zero.
• iv) If each element of a row or column of a determinant is multiplied by a constant k then the value of new determinant is k times the value of the original determinant.
• v) If any two rows or column of a determinant are proportional, then its value is zero.
• vi) If each element of a row or column of a determinant can be expressed as sum of two or more terms, then the determinant can be expressed as the sum of two or more determinants.
• vii) If any row or column of a determinant is added by the multiple of another row or column, the value of the determinant remains same.
• viii) The sum of the products of the elements of any row or column of a determinant with co-factors of the corresponding elements of any other row or column is zero.

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