Math Assignment 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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