Verify the given 7 properties with a suitable matrix (i) Value of the determinant remains unchanged if the rows and columns are interchanged. (ii) If any 2 rows(or columns) are interchanged, sign of the determinant changes. (iii) If all the entries in a row (or column) are zero, then the determinant is zero.
Verify the given 7 properties with a suitable matrix
(i) Value of the determinant remains unchanged if the rows and columns are interchanged.
(ii) If any 2 rows(or columns) are interchanged, sign of the determinant changes.
(iii) If all the entries in a row (or column) are zero, then the determinant is zero.
(iv) If any 2 rows (or columns) of a matrix are identical, the value of the determinant is zero.
(v) If each element of a row (or column) of a matrix is multiplies by a constant k, then value of determinant gets multiplied by k.
(vi) If elements of a row (or column) of a matrix can be expressed as sum of 2(or more) terms, then the determinant can be expressed as sum of 2(or more) determinants.
(vii) If in a matrix all the elements above(or below) the diagonal is zero, (i.e. if the matrix is upper/lower triangular) then the value of the determinant is the product of the diagonal elements
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